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The aim of this work is to develop an effective equation of state for QCD, having the correct asymptotic degrees of freedom, to be used as input for dynamical studies of heavy ion collisions. We present an approach for modeling an EoS that respects the symmetries underlying QCD, and includes the correct asymptotic degrees of freedom, i.e. quarks and gluons at high temperature and hadrons in the low-temperature limit. We achieve this by including quarks degrees of freedom and the thermal contribution of the Polyakov loop in a hadronic chiral sigma-omega model. The hadronic part of the model is a nonlinear realization of an sigma-omega model. As the fundamental symmetries of QCD should also be present in its hadronic states such an approach is widely used to describe hadron properties below and around Tc. The quarks are introduced as thermal quasi particles, coupling to the Polyakov loop, while the dynamics of the Polyakov loop are controlled by a potential term which is fitted to reproduce pure gauge lattice data. In this model the sigma field serves a the order parameter for chiral restoration and the Polyakov loop as order parameter for deconfinement. The hadrons are suppressed at high densities by excluded volume corrections. As a next step, we introduce our new HQ model equation of state in a microscopic+macroscopic hybrid approach to heavy ion collisions. This hybrid approach is based on the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The present implementation allows to compare pure microscopic transport calculations with hydrodynamic calculations using exactly the same initial conditions and freeze-out procedure. The effects of the change in the underlying dynamics - ideal fluid dynamics vs. non-equilibrium transport theory - are explored. The final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The elliptic and directed flow are shown to be not sensitive to changes in the EoS while the smaller mean free path in the hydrodynamic evolution reflects directly in higher flow results which are consistent with the experimental data. This finding indicates qualitatively that physical mechanisms like viscosity and other non equilibrium effects play an essentially more important role than the EoS when bulk observables like flow are investigated. In the last chapter, results for the thermal production of MEMOs in nucleus-nucleus collisions from a combined micro+macro approach are presented. Multiplicities, rapidity and transverse momentum spectra are predicted for Pb+Pb interaction at different beam energies. The presented excitation functions for various MEMO multiplicities show a clear maximum at the upper FAIR energy regime making this facility the ideal place to study the production of these exotic forms of multistrange objects.
In order to fully understand the new state of matter formed in heavy ion collisions, it is vital to isolate the always present final state hadronic contributions within the primary Quark-Gluon Plasma (QGP) experimental signatures. Previously, the hadronic contributions were determined using the properties of the known mesons and baryons. However, according to Hagedorn, hadrons should follow an exponential mass spectrum, which the known hadrons follow only up to masses of M = 2 GeV. Beyond this point the mass spectrum is flat, which indicates that there are "missing" hadrons, that could potentially contribute significantly to experimental observables. In this thesis I investigate the influence of these "missing" Hagedorn states on various experimental signatures of QGP. Strangeness enhancement is considered a signal for QGP because hadronic interactions (even including multi-mesonic reactions) underpredict the hadronic yields (especially for strange particles) at the Relativistic Heavy Ion Collider, RHIC. One can conclude that the time scales to produce the required amount of hadronic yields are too long to allow for the hadrons to reach chemical equilibrium within the lifetime of a cooling hadronic fireball. Because gluon fusion can quickly produce strange quarks, it has been suggested that the hadrons are born into chemical equilibrium following the Quantum Chromodynamics (QCD) phase transition. However, we show here that the missing Hagedorn states provide extra degrees of freedom that can contribute to fast chemical equilibration times for a hadron gas. We develop a dynamical scheme in which possible Hagedorn states contribute to fast chemical equilibration times of X X pairs (where X = p, K, Lambda, or Omega) inside a hadron gas and just below the critical temperature. Within this scheme, we use master equations and derive various analytical estimates for the chemical equilibration times. Applying a Bjorken picture to the expanding fireball, the hadrons can, indeed, quickly chemically equilibrate for both an initial overpopulation or underpopulation of Hagedorn resonances. We compare the thermodynamic properties of our model to recent lattice results and find that for both critical temperatures, Tc = 176 MeV and Tc = 196 MeV, the hadrons can reach chemical equilibrium on very short time scales. Furthermore the ratios p/pi, K/pi , Lambda/pi, and Omega/pi match experimental values well in our dynamical scenario. The effects of the "missing" Hagedorn states are not limited to the chemical equilibration time. Many believe that the new state of matter formed at RHIC is the closet to a perfect fluid found in nature, which implies that it has a small shear viscosity to entropy density ratio close to the bound derived using the uncertainty principle. Our hadron resonance gas model, including the additional Hagedorn states, is used to obtain an upper bound on the shear viscosity to entropy density ratio, eta/s, of hadronic matter near Tc that is close to 1/(4pi). Furthermore, the large trace anomaly and the small speed of sound near Tc computed within this model agree well with recent lattice calculations. We also comment on the behavior of the bulk viscosity to entropy density ratio of hadronic matter close to the phase transition, which qualitatively has a different behavior close to Tc than a hadron gas model with only the known resonances. We show how the measured particle ratios can be used to provide non-trivial information about Tc of the QCD phase transition. This is obtained by including the effects of highly massive Hagedorn resonances on statistical models, which are generally used to describe hadronic yields. The inclusion of the "missing" Hagedorn states creates a dependence of the thermal fits on the Hagedorn temperature, TH , and leads to a slight overall improvement of thermal fits. We find that for Au+Au collisions at RHIC at sqrt{sN N} = 200 GeV the best square fit measure, chi^2 , occurs at TH = Tc = 176 MeV and produces a chemical freeze-out temperature of 172.6 MeV and a baryon chemical potential of 39.7 MeV.
In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. To model the dynamical evolution of the collective system assuming local thermal equilibrium ideal hydrodynamics seems to be a good tool. Nowadays, the development of either viscous hydrodynamic codes or hybrid approaches is favoured. For the microscopic description of the hadronic as well as the partonic stage of the evolution transport approaches have beeen successfully applied, since they generate the full phse-space dynamics of all the particles. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. It constitutes an effective solution of the relativistic Boltzmann equation and is restricted to binary collisions of the propagated hadrons. Therefore, the Boltzmann equation and the basic assumptions of this model are introduced. Furthermore, predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies and the new approach leads to reasonable results over the whole energy range. Studies of phase diagram trajectories using hydrodynamics are performed as a first move into the direction of the development of the hybrid approach. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The initial energy and baryon number density distributions are not smooth and not symmetric in any direction and the initial velocity profiles are non-trivial since they are generated by the non-equilibrium transport approach. The fulll (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. For the present work, three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. Either an in the computational frame isochronous freeze-out or an gradual freeze-out that mimics an iso-eigentime criterion. The particle vectors are generated by Monte Carlo methods according to the Cooper-Frye formula and UrQMD takes care of the final decoupling procedure of the particles. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The elliptic flow values at SPS energies are shown to be in line with an ideal hydrodynamic evolution if a proper initial state is used and the final freeze-out proceeds gradually. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent $v_2$ values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from $E_{\rm lab}=2-160A~$GeV. It is observed that the different freeze-out procedures have almost as much influence on the mean transverse mass excitation function as the equation of state. The experimentally observed step-like behaviour of the mean transverse mass excitation function is only reproduced, if a first order phase transition with a large latent heat is applied or the EoS is effectively softened due to non-equilibrium effects in the hadronic transport calculation. The HBT correlation of the negatively charged pion source created in central Pb+Pb collisions at SPS energies are investigated with the hybrid model. It has been found that the latent heat influences the emission of particles visibly and hence the HBT radii of the pion source. The final hadronic interactions after the hydrodynamic freeze-out are very important for the HBT correlation since a large amount of collisions and decays still takes place during this period.
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.
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
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.
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.
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.