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Abstract: The medium modification of kaon and antikaon masses, compatible with low energy KN scattering data, are studied in a chiral SU(3) model. The mutual interactions with baryons in hot hadronic matter and the e ects from the baryonic Dirac sea on the K( ¯K ) masses are examined. The in-medium masses from the chiral SU(3) e ective model are compared to those from chiral perturbation theory. Furthermore, the influence of these in-medium e ects on kaon rapidity distributions and transverse energy spectra as well as the K, ¯K flow pattern in heavy-ion collision experiments at 1.5 to 2 A·GeV are investigated within the HSD transport approach. Detailed predictions on the transverse momentum and rapidity dependence of directed flow v1 and the elliptic flow v2 are provided for Ni+Ni at 1.93 A·GeV within the various models, that can be used to determine the in-medium K± properties from the experimental side in the near future.
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
Collisions of Si(14.5A GeV+Au are investigated in the relativistic-quantum-molecular-dynamics approach. The calculated pseudorapidity distributions for central collisions compare well with recent experimental data, indicating a large degree of nuclear stopping and thermalization. Nevertheless, nonequilibrium effects play an important role in such complex multihadron reactions: They lead to a strong enhancement of the total kaon production cross sections, in good agreement with the experimental data, without requiring the formation of a deconfined quark-gluon plasma.
The fluid dynamical model is used to study the reactions 20Ne+238U and 40Ar+40Ca at Elab=390 MeV/nucleon. The calculated double differential cross sections d²ð/dΩdE exhibit sidewards maxima in agreement with recent experimental data. The azimuthal dependence of the triple differential distributions, to be obtained from an event-by-event analysis of 4π; exclusive experiments, can yield deeper insight into the collision process: Jets of nuclear matter are predicted with a strongly impact-parameter-dependent thrust angle θjet(b). NUCLEAR REACTIONS Ar+Ca, Ne+U, Elab=393 MeV/nucleon, fluid dynamics with thermal breakup, double differential cross sections, azimuthal dependence of triple differential cross sections, event-by-event thrust analysis of 4π exclusive experiments.
We consider J/ψ production in heavy ion collisions at RHIC energies in the statistical coalescence model with exact (canonical ensemble) charm conservation. Charm quark–antiquark pairs are assumed to be created in primary hard parton collisions, but open and hidden charm particles are formed at the hadronization stage according to the laws of statistical mechanics. The dependence of the J/ψ production on both the number of nucleon participants and the collision energy is studied. The model predicts J/ψ suppression for low energies, whereas at the highest RHIC energy the model reveals J/ψ enhancement.
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.
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 consider the production of the J/psi mesons in heavy ion collisions at RHIC energies in the statistical coalescence model with an exact (canonical ensemble) charm conservation. The cc quark pairs are assumed to be created in the primary hard parton collisions, but the formation of the open and hidden charm particles takes place at the hadronization stage and follows the prescription of statistical mechanics. The dependence of the J/psi production on both the number of nucleon participants and the collision energy is studied. The model predicts the J/psi suppression for low energies, whereas at the highest RHIC energy the model reveals the J/psi enhancement.
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 study the recent claim that the intranuclear cascade model exhibits collective sidewards flow. 4000 intranuclear cascade simulations of the reaction Nb(400 MeV/nucleon)+Nb are performed employing bound and unbound versions of the Cugnon cascade. We show that instability of the target and projectile nuclei in the unbound cascade produces substantial spurious sidewards flow angles, for spectators as well as for participants. Once the nuclear binding is included, the peak of the flow angle distributions for the participants alone is reduced from 35° to 17°. The theoretical ‘‘data’’ are subjected to the experimental multiplicity and efficiency cuts of the plastic ball 4π electronic spectrometer system. The flow angular distributions obtained from the bound cascade—with spectators and participants subjected to the plastic ball filter—are forward peaked, in contrast to the plastic ball data. We discuss the uncertainties encountered with the application of the experimental efficiency and multiplicity filter. The influence of the Pauli principle on the flow is also discussed. The lack of flow effects in the cascade model clearly reflects the absence of the nuclear compression energy that can cause substantially larger collective sidewards motion—there is too little intrinsic pressure built up in the cascade model.
Experimental results are presented on the charge, velocity, and angular distributions of intermediate mass fragments (IMFs) for the reaction Fe+Au at bombarding energies of 50 and 100 MeV/nucleon. Results are compared to the quantum molecular dynamics (QMD) model and a modified QMD which includes a Pauli potential and follows the subsequent statistical decay of excited reaction products. The more complete model gives a good representation of the data and suggests that the major source of IMFs at large angles is due to multifragmentation of the target residue.
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 influence of fluctuations of the shape degree of freedom in collisions of deformed nuclei with energies between 0.8 and 2.1 GeV/nucleon is analyzed on the basis of an intranuclear cascade simulation for the strongly deformed systems 46Ti+ 46Ti and 166Er+ 166Er. While there is a considerable sensitivity of the global event variables to the orientation for polarized beams and targets, this dependence disappears in the average over all orientations for impact parameter selected and integrated events. The dependence of the nuclear stopping and thermalization on the size of the system under consideration and on the bombarding energy is also investigated.
Inclusive neutron spectra were measured at 0°, 4°, 8°, 15°, 30°, and 42° from Nb-Nb and Au-Au collisions at 800 MeV/nucleon. A peak that originates from neutron evaporation from the projectile appears in the spectra at angles out to 8°. The shapes and magnitudes of the spectra are compared with those calculated from models of nucleus-nucleus collisions. The differential cross sections for Au-Au collisions are about four times those for Nb-Nb collisions. The predictions of the Vlasov-Uehling-Uhlenbeck (VUU) and QMD theories agree with the angular distributions of the differential cross sections except at small angles; the VUU prediction overestimates the angular distributions from a few degrees to about 20°, whereas the QMD prediction underestimates the angular distributions below 8°. The Firestreak model overestimates the angular distribution for Nb-Nb collisions and underestimates it for Au-Au collisions. Also, the VUU and QMD models agree with the measured double-differential cross sections in more angular and energy regions than the Firestreak and intranuclear cascade models; however, none of the models can account for the peaks at small angles (θ≤15°).
The in-medium properties of the vector mesons are known to be modified significantly in hot and dense hadronic matter due to vacuum polarisation e ects from the baryon sector in the Walecka model. The vector meson mass drops significantly in the medium due to the e ects of the Dirac sea. In the variational approach adopted in the present paper, these e ects are taken into account through a realignment of the ground state with baryon condensates. Such a realignment of the ground state becomes equivalent to summing of the baryonic tadpole diagrams in the relativistic Hartree approximation (RHA). The approximation scheme adopted here goes beyond RHA to include quantum e ects from the scalar meson and is nonperturbative and self consistent. It includes multiloop e ects, thus corresponding to a di erent approximation as compared to the one loop approximation of including scalar field quantum corrections. In the present work, we study the properties of the vector mesons in the hot and dense matter as modified due to such quantum correction e ects from the baryon as well as scalar meson sectors. These medium modifications of the properties of the vector mesons are reflected, through the shifting and broadening of the respective peaks, in the low mass dilepton spectra. There is broadening of the peaks due to corrections from scalar meson quantum e ects as compared to the relativistic Hartree approximation. It is seen to be rather prominent for the ! meson in the invariant mass plot. PACS number: 21.65.+f,12.40.Yx
A significant drop of the vector meson masses in nuclear matter is observed in a chiral SU(3) model due to the e ects of the baryon Dirac sea. This is taken into account through the summation of baryonic tadpole diagrams in the relativistic Hartree approximation. The appreciable decrease of the in-medium vector meson masses is due to the vacuum polarisation e ects from the nucleon sector and is not observed in the mean field approximation.
We obtain the D-meson spectral density at finite temperature for the conditions of density and temperature expected at FAIR. We perform a self-consistent coupled-channel calculation taking, as a bare interaction, a separable potential model. The Lambda_c (2593) resonance is generated dynamically. We observe that the D-meson spectral density develops a sizeable width while the quasiparticle peak stays close to the free position. The consequences for the D-meson production at FAIR are discussed.
We present an analysis of high energy heavy ion collisions at intermediate impact parameters, using a two-dimensional fluid-dynamical model including shear and bulk viscosity, heat conduction, a realistic treatment of the nuclear binding, and an analysis of the final thermal emission of free nucleons. We find large collective momentum transfer to projectile and target residues (the highly inelastic bounce-off effect) and explosion of the hot compressed shock zones formed during the impact. As the calculated azimuthal dependence of energy spectra and angular distributions of emitted nucleons depends strongly on the coefficients of viscosity and thermal conductivity, future exclusive measurements may allow for an experimental determination of these transport coefficients. The importance of 4π measurements with full azimuthal information is pointed out.
We demonstrate that momentum-dependent nuclear interactions (MDI) have a large effect on the dynamics and on the observables of high-energy heavy-ion collisions: A soft potential with MDI suppresses pion and kaon yields much more strongly than a local hard potential and results in transverse momenta intermediate between soft and hard local potentials. The collective-flow angles and the deuteron-to-proton ratios are rather insensitive to the MDI. Only simultaneous measurements of these observables can give clues on the nuclear equation of state at densities of interest for supernova collapse and neutron-star stability.
Impact parameter dependencies in Pb(160 AGeV)+Pb reactions : hydrodynamical vs. cascade calculations
(1999)
We investigate the impact parameter dependence of the specific entropy S/A in relativistic heavy ion collisions. Especially the anti-Lambda/anti-proton ratio is found to be a useful tool to distinguish between chemical equilibrium assumptions assumed in hydrodynamics (here: the 3-fluid model) and the chemical non-equilibrium scenario like in microscopic models as the UrQMD model.
We study the phase diagram of a generalized chiral SU(3)-flavor model in mean-field approxi- mation. In particular, the influence of the baryon resonances, and their couplings to the scalar and vector fields, on the characteristics of the chiral phase transition as a function of temperature and baryon-chemical potential is investigated. Present and future finite-density lattice calculations might constrain the couplings of the fields to the baryons. The results are compared to recent lattice QCD calculations and it is shown that it is non-trivial to obtain, simultaneously, stable cold nuclear matter.
In this proceeding, we review our recent work using deep convolutional neural network (CNN) to identify the nature of the QCD transition in a hybrid modeling of heavy-ion collisions. Within this hybrid model, a viscous hydrodynamic model is coupled with a hadronic cascade “after-burner”. As a binary classification setup, we employ two different types of equations of state (EoS) of the hot medium in the hydrodynamic evolution. The resulting final-state pion spectra in the transverse momentum and azimuthal angle plane are fed to the neural network as the input data in order to distinguish different EoS. To probe the effects of the fluctuations in the event-by-event spectra, we explore different scenarios for the input data and make a comparison in a systematic way. We observe a clear hierarchy in the predictive power when the network is fed with the event-by-event, cascade-coarse-grained and event-fine-averaged spectra. The carefully-trained neural network can extract high-level features from pion spectra to identify the nature of the QCD transition in a realistic simulation scenario.
In this proceeding we review our recent work using supervised learning with a deep convolutional neural network (CNN) to identify the QCD equation of state (EoS) employed in hydrodynamic modeling of heavy-ion collisions given only final-state particle spectra ρ(pT, Ф). We showed that there is a traceable encoder of the dynamical information from phase structure (EoS) that survives the evolution and exists in the final snapshot, which enables the trained CNN to act as an effective “EoS-meter” in detecting the nature of the QCD transition.
Recent progress in the understanding of the high density phase of neutron stars advances the view that a substantial fraction of the matter consists of hyperons. The possible impacts of a highly attractive interaction between hyperons on the properties of compact stars is investigated. We find that the equation of state exhibits a second stable minimum at large hyperon contents which is in accord with existing hypernuclear data. This second solution gives rise to new effects for neutron star properties which are similar to the ones proposed for the deconfinement transition to strange quark matter and absolutely stable strange stars. We find that the corresponding hyperstars can have rather small radii of R=6-8 km independent of the mass. PACS: 26.60+c, 21.65+f, 97.60.Gb, 97.60.Jd
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 extension of the Periodic System into hitherto unexplored domains - anti- matter and hypermatter - is discussed. Starting from an analysis of hyperon and single hypernuclear properties we investigate the structure of multi-hyperon objects (MEMOs) using an extended relativistic meson field theory. These are contrasted with multi-strange quark states (strangelets). Their production mechanism is stud- ied for relativistic collisions of heavy ions from present day experiments at AGS and SPS to future opportunities at RHIC and LHC. It is pointed out that abso- lutely stable hypermatter is unlikely to be produced in heavy ion collisions. New attention should be focused on short lived metastable hyperclusters ( / 10 10s) and on intensity interferometry of multi-strange-baryon correlations.
We introduce a model for the real-time evolution of a relativistic fluid of quarks coupled to non-equilibrium dynamics of the long wavelength (classical) modes of the chiral condensate. We solve the equations of motion numerically in 3+1 spacetime dimensions. Starting the evolution at high temperature in the symmetric phase, we study dynamical trajectories that either cross the line of first-order phase transitions or evolve through its critical endpoint. For those cases, we predict the behavior of the azimuthal momentum asymmetry for highenergy heavy-ion collisions at nonzero impact parameter.
A generic property of a first-order phase transition in equilibrium, and in the limit of large entropy per unit of conserved charge, is the smallness of the isentropic speed of sound in the mixed phase . A specific prediction is that this should lead to a non-isotropic momentum distribution of nucleons in the reaction plane (for energies < 40A GeV in our model calculation). On the other hand, we show that from present effective theories for low-energy QCD one does not expect the thermal transition rate between various states of the effective potential to be much larger than the expansion rate, questioning the applicability of the idealized Maxwell/Gibbs construction. Experimental data could soon provide essential information on the dynamics of the phase transition.
We discuss the present collective flow signals for the phase transition to quark-gluon plasma (QGP) and the collective flow as a barometer for the equation of state (EoS). A study of Mach shocks induced by fast partonic jets propagating through the QGP is given. We predict a significant deformation of Mach shocks in central Au+Au collisions at RHIC and LHC energies as compared to the case of jet propagation in a static medium. Results of a hydrodynamical study of jet energy loss are presented.
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
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
The properties of pions from the hot and dense reaction stage of relativistic heavy ion collisions are investigated with the quantum molecular dynamics model. Pions originating from this reaction stage stem from resonance decay with enhanced mass. They carry high transverse momenta. The calculation shows a direct correlation between high pt pions, early freeze-out times and high freeze-out densities.
Background: In this interdisciplinary project, the biological effects of heavy ions are compared to those of X-rays using tissue slice culture preparations from rodents and humans. Advantages of this biological model are the conservation of an organotypic environment and the independency from genetic immortalization strategies used to generate cell lines. Its open access allows easy treatment and observation via live-imaging microscopy. Materials and methods: Rat brains and human brain tumor tissue are cut into 300 micro m thick tissue slices. These slices are cultivated using a membrane-based culture system and kept in an incubator at 37°C until treatment. The slices are treated with X-rays at the radiation facility of the University Hospital in Frankfurt at doses of up to 40 Gy. The heavy ion irradiations were performed at the UNILAC facility at GSI with different ions of 11.4 A MeV and fluences ranging from 0.5–10 x 106 particles/cm². Using 3D-confocal microscopy, cell-death and immune cell activation of the irradiated slices are analyzed. Planning of the irradiation experiments is done with simulation programs developed at GSI and FIAS. Results: After receiving a single application of either X-rays or heavy ions, slices were kept in culture for up to 9d post irradiation. DNA damage was visualized using gamma H2AXstaining. Here, a dose-dependent increase and time-dependent decrease could clearly be observed for the X-ray irradiation. Slices irradiated with heavy ions showed less gamma H2AX-positive cells distributed evenly throughout the slice, even though particles were calculated to penetrate only 90–100 micro m into the slice. Conclusions: Single irradiations of brain tissue, even at high doses of 40 Gy, will result neither in tissue damage visible on a macroscopic level nor necrosis. This is in line with the view that the brain is highly radio-resistant. However, DNA damage can be detected very well in tissue slices using gamma H2AX-immuno staining. Thus, slice cultures are an excellent tool to study radiation-induced damage and repair mechanisms in living tissues.
A nonlinear chiral SU(3) approach including the spin 3 2 decuplet is developed to describe dense matter. The coupling constants of the baryon resonances to the scalar mesons are determined from the decuplet vacuum masses and SU(3) symmetry relations. Di erent methods of mass generation show significant differences in the properties of the spin- 3 2 particles and in the nuclear equation of state
We calculate p, ±,K± and (+ 0) rapidity distributions and compare to experimental data from SIS to SPS energies within the UrQMD and HSD transport approaches that are both based on string, quark, diquark (q, ¯q, qq, ¯q ¯q) and hadronic degrees of freedom. The two transport models do not include any explicit phase transition to a quark-gluon plasma (QGP). It is found that both approaches agree rather well with each other and with the experimental rapidity distributions for protons, s, ± and K±. In- spite of this apparent agreement both transport models fail to reproduce the maximum in the excitation function for the ratio K+/ + found experimen- tally between 11 and 40 A·GeV. A comparison to the various experimental data shows that this failure is dominantly due to an insu cient description of pion rapidity distributions rather than missing strangeness . The modest di erences in the transport model results on the other hand can be attributed to di erent implementations of string formation and frag- mentation, that are not su ciently controlled by experimental data for the elementary reactions in vacuum.
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.
We calculate the yields of a variety of hadrons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities di ering strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We calculate the yields of pions, kaons, and Æ-mesons for RHIC and LHC energies assuming thermodynamical equilibration of the produced minijets, and using as input results from pQCD for the energy densities at midrapidity. In the calculation of the production of partons and of transverse energy one has to account for nuclear shadowing. By using two parametrizations for the gluon shadowing one derives energy densities differing strongly in magnitude. In this publication we link those perturbatively calculated energy densities of partons via entropy conservation in an ideal fluid to the hadron multiplicities at chemical freeze-out.
We use 4stout improved staggered lattice data at imaginary chemical potentials to calculate fugacity expansion coefficients in finite temperature QCD. We discuss the phenomenological interpretation of our results within the hadron resonance gas (HRG) model, and the hints they give us about the hadron spectrum. We also discuss features of the higher order coefficients that are not captured by the HRG. This conference contribution is based on our recent papers [1, 2].
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
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.
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.
n this article we will focus on the appearance of the hadron-quark phase transition and the formation of strange matter in the interior region of the hypermassive neutron star and its conjunction with the spectral properties of the emitted gravitational waves (GWs). A strong hadron-quark phase transition might give rise to a mass-radius relation with a twin star shape and we will show in this article that a twin star collapse followed by a twin star oscillation is feasible. If such a twin star collapse would happen during the postmerger phase it will be imprinted in the GW-signal.
Gravitational waves from a core g-mode in supernovae as probes of the high-density equation of state
(2023)
Using relativistic supernova simulations of massive progenitor stars with a quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitational-wave signal that originates from a buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The mode frequency lies in the range 200≲f≲800Hz and decreases with time. As the mode lives in the core of the proto-neutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density.
Gravitational waves from a core g-mode in supernovae as probes of the high-density equation of state
(2023)
Using relativistic supernova simulations of massive progenitor stars with a quark-hadron equation of state (EoS) and a purely hadronic EoS, we identify a distinctive feature in the gravitational-wave signal that originates from a buoyancy-driven mode (g-mode) below the proto-neutron star convection zone. The mode frequency lies in the range 200≲f≲800Hz and decreases with time. As the mode lives in the core of the proto-neutron star, its frequency and power are highly sensitive to the EoS, in particular the sound speed around twice saturation density.
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 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.
The ultrarelativistic quantum molecular dynamics model (UrQMD) is used to study global observables in central reactions of Au+Au at sqrt[s]=200A GeV at the Relativistic Heavy Ion Collider (RHIC). Strong stopping governed by massive particle production is predicted if secondary interactions are taken into account. The underlying string dynamics and the early hadronic decoupling implies only small transverse expansion rates. However, rescattering with mesons is found to act as a source of pressure leading to additional flow of baryons and kaons, while cooling down pions.
Abstract Geant4 is a toolkit for simulating the passage of particles through matter. It includes a complete range of functionality including tracking, geometry, physics models and hits. The physics processes offered cover a comprehensive range, including electromagnetic, hadronic and optical processes, a large set of long-lived particles, materials and elements, over a wide energy range starting, in some cases, from 250 eV and extending in others to the TeV energy range. It has been designed and constructed to expose the physics models utilised, to handle complex geometries, and to enable its easy adaptation for optimal use in different sets of applications. The toolkit is the result of a worldwide collaboration of physicists and software engineers. It has been created exploiting software engineering and object-oriented technology and implemented in the C++ programming language. It has been used in applications in particle physics, nuclear physics, accelerator design, space engineering and medical physics. PACS: 07.05.Tp; 13; 23
The novel momentum analysis technique introduced by Danielewicz and Odyniec can be used to detect and exhibit collective flow in the light system Ar(1800 MeV/nucleon) + KCl where the usual kinetic energy flow analysis fails. The microscopic Vlasov-Uehling-Uhlenbeck theory which includes the nuclear mean field, two-body collisions, and Pauli blocking is used to study this phenomenon. The resulting transverse momentum transfers turn out to be quite sensitive to the nuclear equation of state. From a comparison with experimental data, evidence is presented for a rather stiff nuclear equation of state. The cascade model is unable to describe the data.
The non-equilibrium quantum field dynamics is usually described in the closed-time-path formalism. The initial state correlations are introduced into the generating functional by non-local source terms. We propose a functional approach to the Dyson-Schwinger equation, which treats the non-local and local source terms in the same way. In this approach, the generating functional is formulated for the connected Green functions and one-particle-irreducible vertices. The great advantages of our approach over the widely used two-particle-irreducible method are that it is much simpler and that it is easy to implement the procedure in a computer program to automatically generate the Feynman diagrams for a given process. The method is then applied to a pure gluon plasma to derive the gauge-covariant transport equation from the Dyson-Schwinger equation in the background covariant gauge. We discuss the structure of the kinetic equation and show its relationship with the classical one. We derive the gauge-covariant collision part and present an approximation in the vicinity of equilibrium. The role of the non-local source kernel in the non-equilibrium system is discussed in the context of a free scalar field. PACS numbers: 12.38.Mh, 25.75.-q, 24.85.+p, 11.15.Kc
The recent discovery of binary neutron star mergers has opened a new and exciting venue of research into hot and dense strongly interacting matter. For the first time, this elusive state of matter, described by the theory of quantum chromo dynamics, can be studied in two very different environments. On the macroscopic scale, in the collisions of neutron stars; and on the microscopic scale, in collisions of heavy ions at particle collider facilities. We will discuss the conditions that are created in these mergers and the corresponding high energy nuclear collisions. This includes the properties of quantum chromo dynamics matter, that is, the expected equation of state as well as expected chemical and thermodynamic properties of this exotic matter. To explore this matter in the laboratory, a new research prospect is available at the Facility for Antiproton and Ion Research, FAIR. The new facility is being constructed adjacent to the existing accelerator complex of the GSI Helmholtz Centre for Heavy Ion Research at Darmstadt/Germany, expanding the research goals and technical possibilities substantially. The worldwide unique accelerator and experimental facilities of FAIR will open the way for a broad spectrum of unprecedented research supplying a variety of experiments in hadron, nuclear, atomic, and plasma physics as well as biomedical and material science, which will be briefly described.
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.
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
We present a theoretical description of nuclear collisions which consists of a three-dimensional fluid-dynamical model, a chemical equilibrium breakup calculation for local light fragment (i.e., p, n, d, t, 3He, and 4He) production, and a final thermal evaporation of these particles. The light fragment cross sections and some properties of the heavy target residues are calculated for the asymmetric system Ne+U at 400 MeV/N. The results of the model calculations are compared with recent experimental data. Several observable signatures of the collective hydrodynamical processes are consistent with the present data. An event-by-event analysis of the flow patterns of the various clusters is proposed which can yield deeper insight into the collision dynamics.
The lightest supersymmetric particle, most likely the lightest neutralino, is one of the most prominent particle candidates for cold dark matter (CDM). We show that the primordial spectrum of density fluctuations in neutralino CDM has a sharp cut-off, induced by two different damping mechanisms. During the kinetic decoupling of neutralinos, non-equilibrium processes constitute viscosity effects, which damp or even absorb density perturbations in CDM. After the last scattering of neutralinos, free streaming induces neutralino flows from overdense to underdense regions of space. Both damping mechanisms together define a minimal mass scale for perturbations in neutralino CDM, before the inhomogeneities enter the non- linear epoch of structure formation. We find that the very first gravitationally bound neutralino clouds ought to have masses above 10-6M , which is six orders of magnitude above the mass of possible axion miniclusters.
Subensemble is a type of statistical ensemble which is the generalization of grand canonical and canonical ensembles. The subensemble acceptance method (SAM) provides general formulas to correct the cumulants of distributions in heavy-ion collisions for the global conservation of all QCD charges. The method is applicable for an arbitrary equation of state and sufficiently large systems, such as those created in central collisions of heavy ions. The new fluctuation measures insensitive to global conservation effects are presented. The main results are illustrated in the hadron resonance gas and van der Waals fluid frameworks.
We investigate the hydrodynamical flow of nuclear matter in a conical-shock-wave scenario of a central, asymmetric heavy-ion collision. This work is motivated by a suggestion of Chapline and Granik that the creation of a deconfined phase of quarks and gluons behind the shock will appreciably increase the deflection angle of the matter flow. We employ several hadron matter equations of state recently suggested to solve the conical-shock-wave problem and compare the results with a calculation using the bag equation of state. We find that large differences in the deflection angle obtained in the rest frame of the shock vanish in the laboratory system. However, a signature for the deconfinement transition may be the transverse momentum of the matter flow, which is up to a factor of 2 larger for the quark-gluon plasma. Thus, an excitation function of the mean transverse momentum would show an increase at a certain bombarding energy, signaling the onset of the deconfinement transition.
In power systems, flow allocation (FA) methods enable to allocate the usage and costs of the transmission grid to each single market participant. Based on predefined assumptions, the power flow is split into isolated generator-specific or producer-specific sub-flows. Two prominent FA methods, Marginal Participation (MP) and Equivalent Bilateral Exchanges (EBEs), build upon the linearized power flow and thus on the Power Transfer Distribution Factors (PTDFs). Despite their intuitive and computationally efficient concepts, they are restricted to networks with passive transmission elements only. As soon as a significant number of controllable transmission elements, such as high-voltage direct current (HVDC) lines, operate in the system, they lose their applicability. This work reformulates the two methods in terms of Virtual Injection Patterns (VIPs), which allows one to efficiently introduce a shift parameter q to tune contributions of net sources and net sinks in the network. In this work, major properties and differences in the methods are pointed out, and it is shown how the MP and EBE algorithms can be applied to generic meshed AC-DC electricity grids: by introducing a pseudo-impedance ω¯ , which reflects the operational state of controllable elements and allows one to extend the PTDF matrix under the assumption of knowing the current flow in the system. Basic properties from graph theory are used to solve for the pseudo-impedance in dependence of the position within the network. This directly enables, e.g., HVDC lines to be considered in the MP and EBE algorithms. The extended methods are applied to a low-carbon European network model (PyPSA-EUR) with a spatial resolution of 181 nodes and an 18% transmission expansion compared to today’s total transmission capacity volume. The allocations of MP and EBE show that countries with high wind potentials profit most from the transmission grid expansion. Based on the average usage of transmission system expansion, a method of distributing operational and capital expenditures is proposed. In addition, it is shown how injections from renewable resources strongly drive country-to-country allocations and thus cross-border electricity flows.
In this talk we discuss the effects of the hadronic rescattering on final state observables in high energy nuclear collisions. We do so by employing the UrQMD transport model for a realistic description of the hadronic decoupling process. The rescattering of hadrons modifies every hadronic bulk observable. For example apparent multiplicity of resonances is suppressed as compared to a chemical equilibrium freeze-out model. Stable and unstable particles change their momentum distribution by more than 30% through rescattering. The hadronic rescattering also leads to a substantial decorrelation of the conserved charge distributions. These findings show that it is all but trivial to conclude from the final state observables on the properties of the system at an earlier time where it may have been in or close to local equilibrium.
We estimate the feeddown contributions from decays of unstable A=4 and A=5 nuclei to the final yields of protons, deuterons, tritons, 3He, and 4He produced in relativistic heavy-ion collisions at sNN>2.4 GeV, using the statistical model. The feeddown contribution effects do not exceed 5% at LHC and top RHIC energies due to the large penalty factors involved, but are substantial at intermediate collision energies. We observe large feeddown contributions for tritons, 3He, and 4He at sNN≲10 GeV, where they may account for as much as 70% of the final yield at the lower end of the collision energies considered. Sizable (>10%) effects for deuteron yields are observed at sNN≲4 GeV. The results suggest that the excited nuclei feeddown cannot be neglected in the ongoing and future analysis of light nuclei production at intermediate collision energies, including HADES and CBM experiments at FAIR, NICA at JINR, RHIC beam energy scan and fixed-target programmes, and NA61/SHINE at CERN. We further show that the freeze-out curve in the T-μB plane itself is affected significantly by the light nuclei at high baryochemical potential.
We study the thermodynamic properties of infinite nuclear matter with the Ultrarelativistic Quantum Molecular Dynamics (URQMD), a semiclassical transport model, running in a box with periodic boundary conditions. It appears that the energy density rises faster than T4 at high temperatures of T approx. 200 - 300 MeV. This indicates an increase in the number of degrees of freedom. Moreover, We have calculated direct photon production in Pb+Pb collisions at 160 GeV/u within this model. The direct photon slope from the microscopic calculation equals that from a hydrodynamical calculation without a phase transition in the equation of state of the photon source.
The isospin and strangeness dimensions of the Equation of State are explored. RIA and the SIS200 accelerator at GSI will allow to explore these regions in compressed baryonic matter. 132 Sn + 132 Sn and 100 Sn + 100 Sn collisions as well as the excitation functions of K/pi, Lambda/pi and the centrality dependence of charmonium suppression from the UrQMD and HSD transport models are presented and compared to data. Unambiguous proof for the creation of a 'novel phase of matter' from strangeness and charm yields is not in sight.
The statistical model is used to illustrate the consequences of a successive binary decay mechanism as the initial nuclear excitation is pushed towards the limits of stability. The partition of the excitation energy between light and heavy fragments is explicitly calculated, as are the consequences of the decay of the primary light fragments to particle-bound residual nuclei which would be observed experimentally. The test nucleus 100 44 Ru is considered at initial excitations of 100, 200, 400, and 800 MeV. Exit channels of n, p, and α; and 100 clusters of 3 ≤ Z ≤ 20 ≤ 4, 6 ≤ A ≤ 48 are considered from all nuclides in the deexcitation cascade. The total primary and final cluster yields are shown versus Z and initial excitation. The primary versus final yields are also shown individually for 12C, 26Mg, and 48Ca. We show how multifragmentation yields will change with the excitation energy due to a successive binary decay mechanism. Measurements that may be prone to misinterpretation are discussed, as are those that should be representative of initial nucleus excitation.
The upcoming high energy experiments at the LHC are one of the most outstanding efforts for a better understanding of nature. It is associated with great hopes in the physics community. But there is also some fear in the public, that the conjectured production of mini black holes might lead to a dangerous chain reaction. In this Letter we summarize the most straightforward arguments that are necessary to rule out such doomsday scenarios.
Entropy production in the initial compression stage of relativistic heavy-ion collisions from AGS to SPS energies is calculated within a three-fluid hydrodynamical model. The entropy per participating net baryon is found to increase smoothly and does not exhibit a jump or a plateau as in the 1-dimensional one-fluid shock model. Therefore, the excess of pions per participating net baryon in nucleus-nucleus collisions as compared to proton-proton reactions also increases smoothly with beam energy.
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.
We study the dynamics of high energy heavy ion collisions through the Vlasov-Uehling-Uhlenbeck approach. Equilibration is observed, for central collisions. It is shown that the produced entropy, the pion multiplicity, flow angle, and transverse momentum distributions saturate at the moment of maximum compression and temperature. The effects of the nuclear equation of state and the Pauli principle are investigated. For the flow angle distribution there is a 20 deg reduction of the peak flow angle due to the Pauli principle. A stiff equation of state results in a 10–20 deg increase over the soft equation of state at all energies. The transverse momentum at projectile rapidity exhibits a peak structure as a function of impact parameter b. A 40% difference between soft and hard equation of state is observed for the peak impact parameter, i.e., for intermediate multiplicities.
The study of hidden charm production is an important part of the heavy ion program. The standard approach to this problem [1] assumes that c¯c bound states are created only at the initial stage of the reaction and then partially destroyed at later stages due to interactions with the medium [2, 3, 4].
We investigate transverse hadron spectra from relativistic nucleus-nucleus collisions which reflect important aspects of the dynamics - such as the generation of pressure - in the hot and dense zone formed in the early phase of the reaction. Our analysis is performed within two independent transport approaches (HSD and UrQMD) that are based on quark, diquark, string and hadronic degrees of freedom. Both transport models show their reliability for elementary pp as well as light-ion (C+C, Si+Si) reactions. However, for central Au+Au (Pb+Pb) collisions at bombarding energies above ~ 5 A.GeV the measured K+- transverse mass spectra have a larger inverse slope parameter than expected from the calculation. Thus the pressure generated by hadronic interactions in the transport models above ~ 5 A.GeV is lower than observed in the experimental data. This finding shows that the additional pressure - as expected from lattice QCD calculations at finite quark chemical potential and temperature - is generated by strong partonic interactions in the early phase of central Au+Au (Pb+Pb) collisions.
The recently proposed baryon-strangeness correlation (C_BS) is studied with a string-hadronic transport model (UrQMD) for various energies from E_lab=4 AGeV to \sqrt s=200 AGeV. It is shown that rescattering among secondaries can not mimic the predicted correlation pattern expected for a Quark-Gluon-Plasma. However, we find a strong increase of the C_BS correlation function with decreasing collision energy both for pp and Au+Au/Pb+Pb reactions. For Au+Au reactions at the top RHIC energy (\sqrt s=200 AGeV), the C_BS correlation is constant for all centralities and compatible with the pp result. With increasing width of the rapidity window, C_BS follows roughly the shape of the baryon rapidity distribution. We suggest to study the energy and centrality dependence of C_BS which allow to gain information on the onset of the deconfinement transition in temperature and volume.
Intranuclear cascade calculations and fluid dynamical predictions of the kinetic energy flow are compared for collisions of 40Ca + 40Ca and 238U + 238U. The aspect ratio, R13, as obtained from the global analysis, is independent of the bombarding energy for the intranuclear cascade model. Fluid dynamics, on the other hand, predicts a dramatic increase of R13 at medium energies Elab≲200 MeV/nucleon. In fact, R13(Elab) directly reflects the incompressibility of the nuclear matter and can be used to extract the nuclear equation of stat at high densities. Distortions of the flow tensor due to few nucleon scattering are analyzed. Possible procedures to remove this background from experimental data are discussed.
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
The hypothesis of local equilibrium (LE) in relativistic heavy ion collisions at energies from AGS to RHIC is checked in the microscopic transport model. We find that kinetic, thermal, and chemical equilibration of the expanding hadronic matter is nearly reached in central collisions at AGS energy for t >_ fm/c in a central cell. At these times the equation of state may be approximated by a simple dependence P ~= (0.12-0.15) epsilon. Increasing deviations of the yields and the energy spectra of hadrons from statistical model values are observed for increasing bombarding energies. The origin of these deviations is traced to the irreversible multiparticle decays of strings and many-body (N >_ 3) decays of resonances. The violations of LE indicate that the matter in the cell reaches a steady state instead of idealized equilibrium. The entropy density in the cell is only about 6% smaller than that of the equilibrium state.
Equilibrium properties of infinite relativistic hadron matter are investigated using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model. The simulations are performed in a box with periodic boundary conditions. Equilibration times depend critically on energy and baryon densities. Energy spectra of various hadronic species are shown to be isotropic and consistent with a single temperature in equilibrium. The variation of energy density versus temperature shows a Hagedorn-like behavior with a limiting temperature of 130 +/- 10 MeV. Comparison of abundances of different particle species to ideal hadron gas model predictions show good agreement only if detailed balance is implemented for all channels. At low energy densities, high mass resonances are not relevant; however, their importance raises with increasing energy density. The relevance of these different conceptual frameworks for any interpretation of experimental data is questioned.
The equilibration of hot and dense nuclear matter produced in the central cell of central Au+Au collisions at RHIC (sqrt s = 200 A GeV) energies is studied within a microscopic transport model. The pressure in the cell becomes isotropic at t approx 5 fm/c after beginning of the collision. Within the next 15 fm/c the expansion of matter in the cell proceeds almost isentropically with the entropy per baryon ratio S/A approx 150, and the equation of state in the (P,epsilon) plane has a very simple form, P=0.15 epsilon. Comparison with the statistical model of an ideal hadron gas indicates that the time t approx 20 fm/c may be too short to reach the fully equilibrated state. Particularly, the creation of long-lived resonance-rich matter in the cell decelerates the relaxation to chemical equilibrium. This resonance-abundant state can be detected experimentally after the thermal freeze-out of particles.
A canonical partition function for the two-component excluded volume model is derived, leading to two di erent van der Waals approximations. The one is known as the Lorentz-Berthelot mixture and the other has been proposed recently. Both models are analysed in the canonical and grand canonical ensemble. In comparison with the one-component van der Waals excluded volume model the suppression of particle densities is reduced in these two-component formulations, but in two essentially di erent ways. Presently used multi-component models have no such reduction. They are shown to be not correct when used for components with di erent hard-core radii. For high temperatures the excluded volume interaction is refined by accounting for the Lorentz contraction of the spherical excluded volumes, which leads to a distinct enhancement of lighter particles. The resulting e ects on pion yield ratios are studied for AGS and SPS data.
We study the sensitivities of the directed flow in Au+Au collisions on the equation of state (EoS), employing the transport theoretical model JAM. The EoS is modified by introducing a new collision term in order to control the pressure of a system by appropriately selecting an azimuthal angle in two-body collisions according to a given EoS. It is shown that this approach is an efficient method to modify the EoS in a transport model. The beam energy dependence of the directed flow of protons is examined with two different EoS, a first-order phase transition and crossover. It is found that our approach yields quite similar results as hydrodynamical predictions on the beam energy dependence of the directed flow; Transport theory predicts a minimum in the excitation function of the slope of proton directed flow and does indeed yield negative directed flow, if the EoS with a first-order phase transition is employed. Our result strongly suggests that the highest sensitivity for the critical point can be seen in the beam energy range of 4.7 ≤√sNN≤11.5GeV.
Entropy production in the compression stage of heavy ion collisions is discussed within three distinct macroscopic models (i.e. generalized RHTA, geometrical overlap model and three-fluid hydrodynamics). We find that within these models \sim 80% or more of the experimentally observed final-state entropy is created in the early stage. It is thus likely followed by a nearly isentropic expansion. We employ an equation of state with a first-order phase transition. For low net baryon density, the entropy density exhibits a jump at the phase boundary. However, the excitation function of the specific entropy per net baryon, S/A, does not reflect this jump. This is due to the fact that for final states (of the compression) in the mixed phase, the baryon density \rho_B increases with \sqrt{s}, but not the temperature T. Calculations within the three-fluid model show that a large fraction of the entropy is produced by nuclear shockwaves in the projectile and target. With increasing beam energy, this fraction of S/A decreases. At \sqrt{s}=20 AGeV it is on the order of the entropy of the newly produced particles around midrapidity. Hadron ratios are calculated for the entropy values produced initially at beam energies from 2 to 200 AGeV.
The yields of strange particles are calculated with the UrQMD model for p,Pb(158 AGeV)Pb collisions and compared to experimental data. The yields are enhanced in central collisions if compared to proton induced or peripheral Pb+Pb collisions. The enhancement is due to secondary interactions. Nevertheless, only a reduction of the quark masses or equivalently an increase of the string tension provides an adequate description of the large observed enhancement factors (WA97 and NA49). Furthermore, the yields of unstable strange resonances as the Lambda star(1520) resonance or the phi meson are considerably affected by hadronic rescattering of the decay products.
We discuss the possibility of producing a new kind of nuclear system by putting a few antibaryons inside ordinary nuclei. The structure of such systems is calculated within the relativistic mean field model assuming that the nucleon and antinucleon potentials are related by the G parity transformation. The presence of antinucleons leads to decreasing vector potential and increasing scalar potential for the nucleons. As a result, a strongly bound system of high density is formed. Due to the significant reduction of the available phase space the annihilation probability might be strongly suppressed in such systems.
Enhanced antiproton production in Pb(160 AGeV)+Pb reactions: evidence for quark gluon matter?
(2000)
The centrality dependence of the antiproton per participant ratio is studied in Pb(160 AGeV)+Pb reactions. Antiproton production in collisions of heavy nuclei at the CERN/SPS seems considerably enhanced as compared to conventional hadronic physics, given by the antiproton production rates in pp and antiproton annihilation in p p reactions. This enhancement is consistent with the observation of strong in-medium effects in other hadronic observables and may be an indication of partial restoration of chiral symmetry.
Strong correlations between baryon stopping in the projectile rapidity hemisphere and target excitation have been found in the light-ion-induced reactions at the BNL Alternating Gradient Synchrotron (AGS) (E814 group). Results in the framework of the relativistic molecular dynamics approach (RQMD) describe recent E814 data quite well. We discuss the RQMD results together with proton and pion data from the E802 group near midrapidity. They have raised the question of whether partial transparency could be seen in these experiments. The RQMD results indicate strong transverse baryon flow in central Si+Au collisions after the projectile has been stopped in the target.
Elliptic flow analysis at RHIC with the Lee-Yang Zeroes method in a relativistic transport approach
(2006)
The Lee-Yang zeroes method is applied to study elliptic flow (v_2) in Au+Au collisions at sqrt s =200 A GeV, with the UrQMD model. In this transport approach, the true event plane is known and both the nonflow effects and event-by-event v_2 fluctuations exist. Although the low resolutions prohibit the application of the method for most central and peripheral collisions, the integral and differential elliptic flow from the Lee-Yang zeroes method agrees with the exact v_2 values very well for semi-central collisions.
The cumulant method is applied to study elliptic flow (v_2) in Au+Au collisions at sqrt s=200 AGeV, with the UrQMD model. In this approach, the true event plane is known and both the non-flow effects and event-by-event spatial (epsilon) and v_2 fluctuations exist. Qualitatively, the hierarchy of v_2 's from two, four and six-particle cumulants is consistent with the STAR data, however, the magnitude of v_2 in the UrQMD model is only 60% of the data. We find that the four and six-particle cumulants are good measures of the real elliptic flow over a wide range of centralities except for the most central and very peripheral events. There the cumulant method is affected by the v_2 fluctuations. In mid-central collisions, the four and six-particle cumulants are shown to give a good estimation of the true differential v_2, especially at large transverse momentum, where the two-particle cumulant method is heavily affected by the non-flow effects.
We calculate the antibaryon-to-baryon ratios, anti-p/p, anti-Lambda/Lambda, anti-Xi/Xi, and anti-Omega/Omega for Au+Au collisions at RHIC (sqrt{s}_{NN}=200 GeV). The effects of strong color fields associated with an enhanced strangeness and diquark production probability and with an effective decrease of formation times are investigated. Antibaryon-to-baryon ratios increase with the color field strength. The ratios also increase with the strangeness content |S|. The netbaryon number at midrapidity considerably increases with the color field strength while the netproton number remains roughly the same. This shows that the enhanced baryon transport involves a conversion into the hyperon sector (hyperonization) which can be observed in the (Lambda - anti-Lambda)/(p - anti-p) ratio.
We calculate the antibaryon-to-baryon ratios, p̄/p,Λ̄/Λ,Ξ/Ξ, and Ω/Ω for Au+Au collisions at RHIC (sNN=200 GeV). The effects of strong color fields associated with an enhanced strangeness and diquark production probability and with an effective decrease of formation times are investigated. Antibaryon-to-baryon ratios increase with the color field strength. The ratios also increase with the strangeness content |S|. The netbaryon number at midrapidity considerably increases with the color field strength while the netproton number remains roughly the same. This shows that the enhanced baryon transport involves a conversion into the hyperon sector (hyperonization) which can be observed in the (Λ−Λ̄)/(p−p̄) ratio.
Abstract: The e ect of vacuum fluctuations on the in-medium hadronic properties is investigated using a chiral SU(3) model in the nonlinear realization. The e ect of the baryon Dirac sea is seen to modify hadronic properties and in contrast to a calculation in mean field approximation it is seen to give rise to a significant drop of the vector meson masses in hot and dense matter. This e ect is taken into account through the summation of baryonic tadpole diagrams in the relativistic Hartree approximation (RHA), where the baryon self energy is modified due to interactions with both the non-strange ( ) and the strange ( ) scalar fields.
Effects of a phase transition on HBT correlations in an integrated Boltzmann+hydrodynamics approach
(2009)
A systematic study of HBT radii of pions, produced in heavy ion collisions in the intermediate energy regime (SPS), from an integrated (3+1)d Boltzmann+hydrodynamics approach is presented. The calculations in this hybrid approach, incorporating an hydrodynamic stage into the Ultra-relativistic Quantum Molecular Dynamics transport model, allow for a comparison of different equations of state retaining the same initial conditions and final freeze-out. The results are also compared to the pure cascade transport model calculations in the context of the available data. Furthermore, the effect of different treatments of the hydrodynamic freeze-out procedure on the HBT radii are investigated. It is found that the HBT radii are essentially insensitive to the details of the freeze-out prescription as long as the final hadronic interactions in the cascade are taken into account. The HBT radii RL and RO and the RO/RS ratio are sensitive to the EoS that is employed during the hydrodynamic evolution. We conclude that the increased lifetime in case of a phase transition to a QGP (via a Bag Model equation of state) is not supported by the available data.
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.
We study the effects of isovector-scalar meson delta on the equation of state (EOS) of neutron star matter in strong magnetic fields. The EOS of neutron-star matter and nucleon effective masses are calculated in the framework of Lagrangian field theory, which is solved within the mean-field approximation. From the numerical results one can find that the delta-field leads to a remarkable splitting of proton and neutron effective masses. The strength of delta-field decreases with the increasing of the magnetic field and is little at ultrastrong field. The proton effective mass is highly influenced by magnetic fields, while the effect of magnetic fields on the neutron effective mass is negligible. The EOS turns out to be stiffer at B < 10^15G but becomes softer at stronger magnetic field after including the delta-field. The AMM terms can affect the system merely at ultrastrong magnetic field(B > 10^19G). In the range of 10^15 G - 10^18 G the properties of neutron-star matter are found to be similar with those without magnetic fields.
We want to draw the attention to the dynamics of a (finite) hadronizing quark matter drop. Strange and antistrange quarks do not hadronize at the same time for a baryon-rich system1. Both the hadronic and the quark matter phases enter the strange sector fs 6= 0 of the phase diagram almost immediately, which has up to now been neglected in almost all calculations of the time evolution of the system. Therefore it seems questionable, whether final particle yields reflect the actual thermodynamic properties of the system at a certain stage of the evolution. We put special interest on the possible formation of exotic states, namely strangelets (multistrange quark clusters). They may exist as (meta-)stable exotic isomers of nuclear matter 2. It was speculated that strange matter might exist also as metastable exotic multi-strange (baryonic) objects (MEMO s 3). The possible creation in heavy ion collisions of long-lived remnants of the quark-gluon-plasma, cooled and charged up with strangeness by the emission of pions and kaons, was proposed in 1,4,5. Strangelets can serve as signatures for the creation of a quark gluon plasma. Currently, both at the BNL-AGS and at the CERN-SPS experiments are carried out to search for MEMO s and strangelets, e. g. by the E864, E878 and the NA52 collaborations9,
Dynamics of strange, charm and high momentum hadrons in relativistic nucleus nucleus collisions
(2003)
We investigate hadron production and attenuation of hadrons with strange and charm quarks (or antiquarks) as well as high transverse momentum hadrons in relativistic nucleus-nucleus col- lisions from 2 A·GeV to 21.3 A·TeV within two independent transport approaches (UrQMD and HSD). Both transport models are based on quark, diquark, string and hadronic degrees of freedom, but do not include any explicit phase transition to a quark-gluon plasma. From our dynamical calculations we find that both models do not describe the maximum in the K+/ + ratio at 20 - 30 A·GeV in central Au+Au collisions found experimentally, though the excitation functions of strange mesons are reproduced well in HSD and UrQMD. Furthermore, the transport calculations show that the charmonium recreation by D + J/ + meson reactions is comparable to the dissociation by comoving mesons at RHIC energies contrary to SPS energies. This leads to the final result that the total J/ suppression as a function of centrality at RHIC should be less than the suppression seen at SPS energies where the comover dissociation is substantial and the backward channels play no role. Furthermore, our transport calculations in comparison to exper- imental data on transverse momentum spectra from pp, d+Au and Au+Au reactions show that pre-hadronic e ects are responsible for both the hardening of the hadron spectra for low transverse momenta (Cronin e ect) as well as the suppression of high pT hadrons. The mutual interactions of formed hadrons are found to be negligible in central Au+Au collisions at s = 200 GeV for pT e 6 GeV/c and the sizeable suppression seen experimentally is attributed to a large extent to the interactions of leading pre-hadrons with the dense environment.
Yields, rapidity and transverse momentum spectra of Delta++(1232), Lambda(1520), Sigma+-(1385) and the meson resonances K0(892), Phi, rho0 and f0(980) are predicted. Hadronic rescattering leads to a suppression of reconstructable resonances, especially at low p_perp. A mass shift of the rho of 10 MeV is obtained from the microscopic simulation, due to late stage rho formation in the cooling pion gas.
A quasiclassical Pauli potential is used to simulate the Fermi motion of nucleons in a molecular dynamical simulation of heavy ion collisions. The thermostatic properties of a Fermi gas with and without interactions are presented. The inclusion of this Pauli potential into the quantum molecular dynamics (QMD) approach yields a model with well defined fermionic ground states, which is therefore also able to give the excitation energies of the emitted fragments. The deexcitation mechanisms (particle evaporation and multifragmentation) of the new model are investigated. The dynamics of the QMD with Pauli potential is tested by a wide range of comparisons of calculated and experimental double-differential cross sections for inclusive p-induced reactions at incident energies of 80 to 160 MeV. Results at 256 and 800 MeV incident proton energy are presented as predictions for completed experiments which are as yet unpublished.
We calculate the evolution of quark-gluon-plasma droplets during the hadronization in a thermodynamical model. It is speculated that cooling as well as strangeness enrichment allow for the formation of strangelets even at very high initial entropy per baryon S/Ainit H 500 and low initial baryon numbers of Ainit B H 30. It is shown that the droplet with vanishing initial chemical potential of strange quarks and a very moderate chemical potential of up/down quarks immediately charges up with strangeness. Baryon densi- ties of H 2 0 and strange chemical potentials of µs > 350 MeV are reached if strangelets are stable. The importance of net baryon and net strangeness fluctuations for the possible strangelet formation at RHIC and LHC is em- phasized. Pacs-Classif.: 25.15.tr, 12.38.Mh, 24.85.tp
Distillation and survival of strange quark matter droplets in ultrarelativistic heavy ion collisions
(1991)
Recently it has been suggested that rather cold droplets of absolutely stable or metastable strange-quark matter may be distilled in heavy-ion collisions during the phase transition from a baryon-rich quark-gluon plasma (QGP) to hadron matter. Here we present a model describing the hadronization of the QGP through particle emission, which is based solely on thermodynamical arguments. Pions and K+’s and K0’s carry away entropy and antistrangeness from the system, thus facilitating the cooling process and the strangelet formation. Our results are supported by revised more sophisticated rate calculations. Two rather unexpected results are obtained when this model is applied to the investigation of strangelet production. The strangeness separation mechanism and the formation process works well even for higher initial entropies per baryon, tantamount to higher bombarding energies. The surviving strangelets have a rather high strangeness content, fs∼1.2–2 [i.e., Z/A∼(-0.1)–(-0.5)]. Hence droplets of strange-quark matter with a baryon number of ∼10–30 and with a negative charge may be produced. They may serve as a unique signature for the transient formation of a quark-gluon plasma in heavy-ion collisions.