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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
Nuclear transport models including density- and momentum-dependent mean-field effects are compared to intranuclear-cascade models and tested on recent data on inclusive p-like cross sections for 800A-MeV La+La. We find a remarkable agreement between most model calculations but a systematic disagreement with the measured yield at 20°, possibly indicating a need for modification of nuclear transport properties at high densities.
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.
Study of hard core repulsive interactions in an hadronic gas from a comparison with lattice QCD
(2016)
We study the influence of hard-core repulsive interactions within the Hadron-Resonace Gas model in comparison to first principle calculation performed on a lattice. We check the effect of a bag-like parametrization for particle eigenvolume on flavor correlators, looking for an extension of the agreement with lattice simulations up to higher temperatures, as was yet pointed out in an analysis of hadron yields measured by the ALICE experiment. Hints for a flavor depending eigenvolume are present.
The Monte Carlo parton string model for multiparticle production in hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions at high energies is described. An adequate choice of the parameters in the model gives the possibility of recovering the main results of the dual parton model, with the advantage of treating both hadron and nuclear interactions on the same footing, reducing them to interactions between partons. Also the possibility of considering both soft and hard parton interactions is introduced.
The thermodynamic properties of the interacting particle–antiparticle boson system at high temperatures and densities were investigated within the framework of scalar and thermodynamic mean-field models. We assume isospin (charge) density conservation in the system. The equations of state and thermodynamic functions are determined after solving the self-consistent equations. We study the relationship between attractive and repulsive forces in the system and the influence of these interactions on the thermodynamic properties of the bosonic system, especially on the development of the Bose–Einstein condensate. It is shown that under “weak” attraction, the boson system has a phase transition of the second order, which occurs every time the dependence of the particle density crosses the critical curve or even touches it. It was found that with a “strong” attractive interaction, the system forms a Bose condensate during a phase transition of the first order, and, despite the finite value of the isospin density, these condensate states are characterized by a zero chemical potential. That is, such condensate states cannot be described by the grand canonical ensemble since the chemical potential is involved in the conditions of condensate formation, so it cannot be a free variable when the system is in the condensate phase.
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
In fluid dynamical models the freeze out of particles across a three dimensional space-time hypersurface is discussed. The calculation of final momentum distribution of emitted particles is described for freeze out surfaces, with both space-like and time-like normals, taking into account conservation laws across the freeze out discontinuity.
In this paper, the concepts of microscopic transport theory are introduced and the features and shortcomings of the most commonly used ansatzes are discussed. In particular, the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model is described in great detail. Based on the same principles as QMD and RQMD, it incorporates a vastly extended collision term with full baryon-antibaryon symmetry, 55 baryon and 32 meson species. Isospin is explicitly treated for all hadrons. The range of applicability stretches from E lab < 100$ MeV/nucleon up to E lab> 200$ GeV/nucleon, allowing for a consistent calculation of excitation functions from the intermediate energy domain up to ultrarelativistic energies. The main physics topics under discussion are stopping, particle production and collective flow.
Ratios of hadronic abundances are analyzed for pp and nucleus-nucleus collisions at sqrt(s)=20 GeV using the microscopic transport model UrQMD. Secondary interactions significantly change the primordial hadronic cocktail of the system. A comparison to data shows a strong dependence on rapidity. Without assuming thermal and chemical equilibrium, predicted hadron yields and ratios agree with many of the data, the few observed discrepancies are discussed.
Accurate impact parameter determination in a heavy-ion collision is crucial for almost all further analysis. We investigate the capabilities of an artificial neural network in that respect. First results show that the neural network is capable of improving the accuracy of the impact parameter determination based on observables such as the flow angle, the average directed inplane transverse momentum and the difference between transverse and longitudinal momenta. However, further investigations are necessary to discover the full potential of the neural network approach.
Abstract: An accurate impact parameter determination in a heavy ion collision is crucial for almost all further analysis. The capabilities of an artificial neural network are investigated to that respect. A novel input generation for the network is proposed, namely the transverse and longitudinal momentum distribution of all outgoing (or actually detectable) particles. The neural network approach yields an improvement in performance of a factor of two as compared to classical techniques. To achieve this improvement simple network architectures and a 5 × 5 input grid in (pt, pz) space are suffcient.
We 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.
Signatures of quark gluon plasma formation in high-energy heavy ion collisions : a critical review
(1998)
Ultra-relativistic heavy ion collisions offer the unique opportunity to probe highly excited dense nuclear matter under controlled laboratory conditions. The compelling driving force for such studies is the expectation that an entirely new form of matter may be created from such reactions. That form of matter, called the Quark Gluon Plasma (QGP), is the QCD analogue of the plasma phase of ordinary atomic matter. However, unlike such ordinary plasmas, the deconfined quanta of a QGP are not directly observable because of the fundamental confining property of the physical QCD vacuum. What is observable are hadronic and leptonic residues of the transient QGP state. There is a large variety of such individual probes.
Triple differential cross sections of pions in heavy ion collisions at 1 GeV/nucl. are studied with the IQMD model. After discussing general properties of resonance and pion production we focus on azimuthal correlations: At projectile- and target-rapidities we observe an anticorrelation in the in-plane transverse momentum between pions and protons. At c.m.-rapidity, however, we find that high pt pions are being preferentially emitted perpendicular to the event-plane. We investigate the causes of those correlations and their sensitivity on the density and momentum dependence of the real and imaginary part of the nucleon and pion optical potential.
We investigate the sensivity of pionic bounce-off and squeeze-out on the density and momentum dependence of the real part of the nucleon optical potential. For the in-plane pion bounce-off we find a strong sensivity on both the density and momentum dependence whereas the out-of-plane pion squeeze-out shows a strong sensivity only towards the momentum dependence but little sensivity towards the density dependence.
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.
Azimuthal correlations of pions are studied with the quantum molecular dynamics model. Pions are preferentially emitted perpendicular to the reaction plane. Our analysis shows that this anisotropy is dominated by pion absorption on the spectator matter in the reaction plane. Pions emitted perpendicular to the reaction plane undergo less rescattering than those emitted in the reaction plane and might therefore be more sensitive to the early hot and dense reaction phase.
We introduce a transport approach which combines partonic and hadronic degrees of freedom on an equal footing and discuss the resulting reaction dynamics. The initial parton dynamics is modeled in the framework of the parton cascade model, hadronization is performed via a cluster hadronization model and configuration space coalescence, and the hadronic phase is described by a microscopic hadronic transport approach. The resulting reaction dynamics indicates a strong influence of hadronic rescattering on the space-time pattern of hadronic freeze-out and on the shape of transverse mass spectra. Freeze-out times and transverse radii increase by factors of 2 3 depending on the hadron species.
We analyze the reaction dynamics of central Pb+Pb collisions at 160 GeV/nucleon. First we estimate the energy density pile-up at mid-rapidity and calculate its excitation function: The energy density 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 E >= 30 GeV/nucleon. The energy density reaches up to 4 GeV/fm 3, 95% of which are contained in partonic degrees of freedom. It is shown that cells of hadronic matter, after the early reaction phase, can be viewed as nearly chemically equilibrated. This matter never exceeds energy densities of 0.4 GeV/fm 3, i.e. a density above which the notion of separated hadrons loses its meaning. The final reaction stage is analyzed in terms of hadron ratios, freeze-out distributions and a source analysis for final state pions.
A model based on chiral SU(3)-symmetry in nonlinear realisation is used for the investigation of nuclei, superheavy nuclei, hypernuclei and multistrange nuclear objects (so called MEMOs). The model works very well in the case of nuclei and hypernuclei with one Lambda-particle and rules out MEMOs. Basic observables which are known for nuclei and hypernuclei are reproduced satisfactorily. The model predicts Z=120 and N=172, 184 and 198 as the next shell closures in the region of superheavy nuclei. The calculations have been performed in self-consistent relativistic mean field approximation assuming spherical symmetry. The parameters were adapted to known nuclei.
We investigate event-by-event fluctuations for ensembles with non-fixed multiplicity. Moments of event observable distributions, like total energy distribution, total transverse momentum distribution, etc, are shown to be related to the multi-body correlations present in the system. For classical systems, these moments reduce in the absence of any correlations to the mo- ments of particle inclusive momentum distribution. As a consequence, a zero value for the recently introduced Phi-variable is shown to indicate the van- ishing of two-body correlations from one part, and of correlations between multiplicity and momentum distributions from the other part. It is often misunderstood as a measure of the degree of equilibration in the system.
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.
An extension to the Einstein–Cartan (EC) action is discussed in terms of cosmological solutions. The torsion incorporated in the EC Lagrangian is assumed to be totally anti-symmetric, represented by a time-like axial vector Sμ. The dynamics of torsion is invoked by a novel kinetic term. Here we show that this kinetic term gives rise to dark energy, while the quadratic torsion term, emanating from the EC part, represents a stiff fluid that leads to a bouncing cosmology solution. A constraint on the bouncing solution is calculated using cosmological data from different epochs.
Bounding Dark Energy from the SPARC rotation curves: Data driven probe for galaxy virialization
(2024)
Dark Energy (DE) acts as a repulsive force that opposes gravitational attraction. Assuming galaxies maintain a steady state over extended periods, the estimated upper bound on DE studies its resistance to the attractive gravitational force from dark matter. Using the SPARC dataset, we fit the Navarro-Frenk-White (NFW) and Hernquist models to identify the most suitable galaxies for these models. Introducing the presence of DE in these galaxies helps establish the upper limit on its repulsive force. This upper bound on DE sits around ρ(<Λ)∼10−25~kg/m3, only two orders of magnitude higher than the one measured by Planck. We discuss the conditions for detecting DE in different systems and show the consistency of the upper bound from galaxies to other systems. The upper bound is of the same order of magnitude as ρ200=200ρc for both dark matter profiles. We also address the implications for future measurements on that upper bound and the condition for detecting the impact of Λ on galactic scales.
Stopping power and thermalization in relativistic heavy ion collisions is investigated employing the quantum molecular dynamics approach. For heavy systems stopping of the incoming nuclei is predicted, independent of the energy. The influence of the quantum effects and their increasing importance at low energies, is demonstrated by inspection of the mean free path of the nucleons and the n-n collision number. Classical models, which neglect these effects, overestimate the stopping and the thermalization as well as the collective flow and squeeze out. The sensitivity of the transverse and longitudinal momentum transfer to the in-medium cross section and to the pressure is investigated.
We examine experimental signatures of TeV-mass black hole formation in heavy ion collisions at the LHC. We find that the black hole production results in a complete disappearance of all very high p_T (> 500 GeV) back-to-back correlated di-jets of total mass M > M_f ~ 1 TeV. We show that the subsequent Hawking-decay produces multiple hard mono-jets and discuss their detection. We study the possibility of cold black hole remnant (BHR) formation of mass ~ M_f and the experimental distinguishability of scenarios with BHRs and those with complete black hole decay. Finally we point out that a Heckler-Kapusta-Hawking plasma may form from the emitted mono-jets. In this context we present new simulation data of Mach shocks and of the evolution of initial conditions until the freeze-out.
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 microscopic phasespace approach URQMD is used to investigate the stopping power and particle production in heavy systems at SPS and RHIC energies. We find no gap in the baryon rapidity distribution even at RHIC. For CERN energies URQMD shows a pile up of baryons and a supression of multi-nucleon clusters at midrapidity.
Microscopic calculations of central collisions between heavy nuclei are used to study fragment production and the creation of collective flow. It is shown that the final phase space distributions are compatible with the expectations from a thermally equilibrated source, which in addition exhibits a collective transverse expansion. However, the microscopic analyses of the transient states in the reaction stages of highest density and during the expansion show that the system does not reach global equilibrium. Even if a considerable amount of equilibration is assumed, the connection of the measurable final state to the macroscopic parameters, e.g. the temperature, of the transient "equilibrium" state remains ambiguous.
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.
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.
We perform an event-by-event analysis of the transverse momentum distribution of final state particles in central Pb(160AGeV)+Pb collisions within a microscopic non-equilibrium transport model (UrQMD). Strong influence of rescattering is found. The extracted momentum distributions show less fluctuations in A+A collisions than in p+p reactions. This is in contrast to simplified p+p extrapolations and random walk models.
In ultra-relativistic heavy ion collisions, early stage multiple scatterings may lead to an increase of the color electric field strength. Consequently, particle production - especially heavy quark (and di-quark) production - is greatly enhanced according to the Schwinger mechanism. We test this idea via the Ultra-relativistic Quantum Molecular Dynamics model (UrQMD) for Au+Au collisions at the full RHIC energy (ps = 200 AGeV). Relative to p+p collisions, a factor of 60, 20 and 7 enhancement respectively, for (sss), (ss), and , (s) is predicted for a model with increased color electric field strength.
In the framework of the relativistic quantum molecular dynamics approach (RQMD) we investigate antideuteron (d) observables in Au+Au collisions at 10.7 AGeV. The impact parameter dependence of the formation ratios d/p2 and d/p2 is calculated. In central collisions, the antideuteron formation ratio is predicted to be two orders of magnitude lower than the deuteron formation ratio. The d yield in central Au+Au collisions is one order of magnitude lower than in Si+Al collisions. In semicentral collisions di erent configuration space distributions of p s and d s lead to a large squeeze out e ect for antideuterons, which is not predicted for the p s.
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 sign reversal of the directed flow parameter v1 in the central rapidity region in Au+Au collisions at s = 200 AGeV is predicted. This anti-flow is shown to be linked to the expansion of the hot matter created. In line with this observation the predicted elliptic flow parameter v2 of various particle species is linked to the mean free path of these particles.
Schwarze Löcher im Labor? : Auf der Suche nach einer experimentellen Bestätigung der Stringtheorie
(2006)
Schwarze Löcher – das sind im Allgemeinen alles verschlingende, gigantisch schwere astronomische Objekte mit bis zu einigen Milliarden Sonnenmassen. Am Frankfurt Institute for Advanced Studies (FIAS) und am Institut für Theoretische Physik sind in den vergangenen fünf Jahren eine ganz neue Art von Schwarzen Löchern theoretisch vorhergesagt worden, die genau das Gegenteil der astronomisch gemessenen Giganten darstellen, nämlich winzig kleine Schwarze Löcher, so genannte »mini black holes«. Auftreten könnten sie, wenn im kommenden Jahr der neue Teilchenbeschleuniger am CERN in Genf in Betrieb genommen wird.
Relativistic hadron-hadron collisions in the ultra-relativistic quantum molecular dynamics model
(1999)
Hadron-hadron collisions at high energies are investigated in the Ultra- relativistic-Quantum-Molecular-Dynamics approach. This microscopic trans- port model describes the phenomenology of hadronic interactions at low and intermediate energies ( s < 5 GeV) in terms of interactions between known hadrons and their resonances. At higher energies, s > 5 GeV, the excitation of color strings and their subsequent fragmentation into hadrons dominates the multiple production of particles in the UrQMD model. The model shows a fair overall agreement with a large body of experimental h-h data over a wide range of h-h center-of-mass energies. Hadronic reaction data with higher precision would be useful to support the use of the UrQMD model for relativistic heavy ion collisions.
We investigate the onset of multifragmentation employing an improved version of the N-body ‘‘quantum’’ molecular-dynamics approach. We study in detail the reaction 18O+197Au at 84 MeV/nucleon and find good agreement between the calculated results and the data for the double-differential proton cross section, the mass yield, the multiplicity, the kinetic energy of the fragments, and even for the kinematic correlations between intermediate mass fragments (IMF’s), which have been measured in this experiment for the first time. We observe a strong correlation between the impact parameter and both the size of the target remnant as well as the average proton multiplicity. Hence both observables can be used to determine the impact parameter experimentally. The IMF’s come from the most central collisions. The calculations confirm the experimental result that they are not emitted from an equilibrated system. Although the inclusive energy spectra look thermal, we cannot identify an impact parameter-independent isotropically emitting source. Even in central collisions global equilibrium is not observed. We find that multifragment emission at this bombarding energy is caused by a process very similar to that proposed in the macroscopic cold multifragmentation model. Thus it has a different origin than at beam energies around 1 GeV/nucleon, although the mass yield has an almost identical slope.
Abstract: We study transverse expansion and directed flow in Au(11AGeV)Au reactions within a multi-fluid dynamical model. Although we do not employ an equation of state (EoS) with a first order phase transition, we find a slow increase of the transverse velocities of the nucleons with time. A similar behaviour can be observed for the directed nucleon flow. This is due to non-equilibrium e ects which also lead to less and slower conversion of longitudinal into transverse momentum. We also show that the proton rapidity distribution at CERN energies, as calculated within this model, agrees well with the preliminary NA44-data.
To describe ultrarelativistic heavy-ion collisions we construct a three-fluid hydrodynamical model. In contrast to one-fluid hydrodynamics, it accounts for the finite stopping power of nuclear matter, i.e. for nonequilibrium e ects in the early stage of the reaction. Within this model, we study baryon dynamics in the BNL-AGS energy range. For the system Au+Au we find that kinetic equilibrium between projectile and target nucleons is established only after a time teq CM H 5 fm/c C 2RAu/³CM. Observables which are sensitive to the early stage of the collision (like e.g. nucleon flow) therefore di er considerably from those calculated in the one-fluid model.