Parton cascade is a microscopic transport approach for the study of the space-time evolution of the Quark-Gluon Plasma produced in relativistic heavy ion collisions and its experimental manifestations. In the following, parton cascade calculations on elliptic flow and thermalization will be discussed. Dynamical evolution is shown to be important for the production of elliptic flow including the scaling and the breaking of the scaling of elliptic flow. The degree of thermalization is estimated using both an elastic parton cascade and a radiative transport model. A longitudinal to transverse pressure ratio, $P_L/P_T\approx 0.8$, is shown to be expected in the central cell in central collisions. This provides information on viscous corrections to the ideal hydrodynamical approach.
A parton-hadron cascade model which is the extension of hadronic cascade model incorporating hard partonic scattering based on HIJING is presented to describe the space-time evolution of parton/hadron system produced by ultra-relativistic nuclear collisions. Hadron yield, baryon stopping and transverse momentum distribution are calculated and compared with HIJING and VNI.
A Monte Carlo program solving Boltzmann equation for partons via cascade method is presented. At presented, only gluon-gluon elastic scattering is included. The scattering cross section is regulated by a medium generated screening mass. Three different geometric modes (3 dimension expansion, 1-d expansion, and scattering inside a box) are provided for theoretical study of the parton transport and the applicability of the cascade method. Space cell division is available to save the number of computer operations. This improves the speed of the calculation by a large factor and makes the code bes…
The dependence of elliptic flow at RHIC energies on the effective parton scattering cross section is calculated using the ZPC parton cascade model. We show that the v_2 measure of elliptic flow saturates early in the evolution before the hadronization transition to a rather large value ~0.05-0.15 as σ_g varies from 2-10 mb and thus is a sensitive probe of the dynamics in the plasma phase.
The baryon distribution is studied by using a parton cascade model which is based on pQCD incorporating hard partonic scattering and dynamical hadronization scheme. In order to study baryon distribution,baryonic cluster formation is newly implemented as well as hadronic higher resonance states from parton/beam cluster decay. The net baryon number and charged hadron distributions are calculated with different $K$-factors in which parameters are fixed by elementary $p\bar p$ data at $E_{c.m.}=200$ GeV. It is found that baryon stopping behavior at SPS and RHIC energies are not consequence of hard…
We utilize the Parton Cascade Model to study the evolution of charm quarks propagating through a thermal brick of QCD matter. We determine the energy loss and the transport coefficient '$\hat{q}$' for charm quarks. The calculations are done at a constant temperature of 350 MeV and the results are compared to analytical calculations of heavy quark energy loss in order to validate the applicability of using a Parton Cascade Model for the study of heavy quarks dynamics in hot and dense QCD matter.
This is a review of the parton cascade model (PCM) which provides a QCD-based description of nucleus-nucleus reactions at very high energy. The PCM describes the collision dynamics within the early and dense phase of the reaction in terms of the relativistic, probabilistic transport of perturbative excitations (partons) of the QCD vacuum, combined with the renormalization group flow of the parton virtuality. The current state of numerical implementations of the model, as well as its predictions for nuclear collisions at RHIC and LHC are discussed.
Frame dependence of parton cascade results is studied for different schemes of doing cascade simulations. We show that different schemes do not always agree and results may have strong frame dependence. When the interaction range is on the order of mean free path and the collisions are done in the two particle center of mass frame, the results are not sensitive to the global frame that the collisions are ordered. Effects of different differential cross sections are also discussed.
We develop two further numerical tests of parton cascade models: the ideal gas equation of state and the collision frequency tests. The equation of state test checks the initial momentum distribution generator and free expansion dynamics in periodic inhomogeneous geometries. The collision rate test is sensitive to spatial inhomogeneities and the collision algorithm. These tests are applied to the recently developed ZPC parton cascade model. The tests helped uncover unphysical correlations induced by one of the commonly used random number generators and showed the necessity of particle subdivis…
We have updated the parton and hadron cascade model PACIAE for the relativistic nuclear collisions, from based on JETSET 6.4 and PYTHIA 5.7 to based on PYTHIA 6.4, and renamed as PACIAE 2.0. The main physics concerning the stages of the parton initiation, parton rescattering, hadronization, and hadron rescattering were discussed. The structures of the programs were briefly explained. In addition, some calculated examples were compared with the experimental data. It turns out that this model (program) works well.
We study pre-equilibrium strangeness production at RHIC energies in a new parton cascade. Starting with the turbulent glue HIJING initial conditions we investigate the interplay between mini-jet and soft beam jet gluons for strangeness production prior to hadronization, and show the importance of soft beam jet gluons in the strangeness production.
Differential elliptic flow out to p_t ~ 5 GeV/c is calculated using the MPC elastic parton cascade model for Au+Au at Ecm ~ 130A GeV. The results are compared to recent STAR/RHIC elliptic flow data. An elliptic flow pattern comparable to the data seems to require initial parton densities at least twice higher than predicted by the HIJING model. Elliptic flow is also shown to be sensitive to the hadronization procedure.
Differential elliptic flow out to p_T ~ 5 GeV/c and particle spectra are calculated using the MPC elastic parton cascade model for Au+Au at Ecm ~ 130A GeV. The evolution is computed from parton transport theory, followed by hadronization either via independent fragmentation or by imposing parton-hadron duality. With pQCD elastic cross sections, very large initial gluon densities dN/deta > 7000 are required to reproduce the data measured by the STAR collaboration. In addition, elliptic flow and the p_T spectra are shown to be very sensit ive to particle subdivision.
I review Klaus Kinder-Geiger's contributions to the physics of relativistic heavy ion collisions, in particular, the Parton Cascade Model. Klaus developed this model in order to provide a QCD-based description of nucleus-nucleus reactions at high energies such as they will soon become available at the Brookhaven Relativistic Heavy Ion Collider. The PCM describes the collision dynamics within the early and dense phase of the reaction in terms of the relativistic, probabilistic transport of perturbative excitations (partons) of the QCD vacuum. I will present an overview of the current state of t…
The transverse profile dependence of elliptic flow is studied in a parton cascade model. We compare results from the binary scaling profile to results from the wounded nucleon scaling profile. The impact parameter dependence of elliptic flow is shown to depend sensitively on the transverse profile of initial particles, however, if elliptic flow is plotted as a function of the relative multiplicity, the nuclear profile dependence disappears. The insensitivity was found previously in a hydrodynamical calculation. Our calculations indicate that the insensitivity is also valid with additional visc…
We consider the evolution of a parton system which is formed at the central rapidity region just after an ultrarelativistic heavy ion collision. The evolution of the system, which is composed of gluons, quarks and antiquarks, is described by a relativistic Boltzmann equations with collision terms including radiation and retardation effects. The equations are solved by the test particle method using Monte-Carlo sampling. Our simulations do not show any evidence of kinetic equilibration, unless the cross sections are artificially increased to unrealistically large values.
We propose a test of Monte Carlo Parton Cascade models based on analytic solutions of covariant kinetic theory for longitudinally boost and transverse translation invariant boundary conditions. We compute the evolution of the transverse energy per unit rapidity for typical mini-jet initial conditions expected in ultra-relativistic nuclear collisions. The kinetic theory solutions under these conditions test the models severely because they deviate strongly from free-streaming and also from ideal Euler and dissipative Navier-Stokes hydrodynamical approximations. We show that the newly formulated…
We study the production and dynamics of heavy quarks in the parton cascade model for relativistic heavy ion collisions. The model is motivated by the QCD parton picture and describes the dynamics of an ultra-relativistic heavy-ion collision in terms of cascading partons which undergo scattering and multiplication while propagating. We focus on the dynamics of charm quark production and evolution in p+p and Au+Au collisions for several different interaction scenarios, i.e. collisions only between primary partons without radiation of gluons, multiple collisions without radiation of gluons and mu…
This comment is withdrawn, as the figure on which it was based is inconsistent with other figures in the text and thus probably incorrect. Using the other figures, I find that the parton cascade model does approach chemical equilibrium correctly.
We study the impact of the Landau Pomeranchuk Midgal (LPM) effect on the dynamics of parton interactions in proton proton collisions at the Large Hadron Collider energies. For our investigation we utilize a microscopic kinetic theory based on the Boltzmann equation. The calculation traces the space-time evolution of the cascading partons interacting via semihard pQCD scatterings and fragmentations. We focus on the impact of the LPM effect on the production of charm quarks, since their production is exclusively governed by processes well described in our kinetic theory. The LPM effect is found …
In view of the recent WA98 data of pi0 spectra from central Pb+Pb collisions at the CERN SPS, we analyze the production of neutral pions for A+$ collisions across the periodic table at sqrt(s)=17 AGeV and 200 AGeV within the framework of the parton-cascade model for relativistic heavy ion collisions. The multiplicity of the pions (having pT > 0.5 GeV/c) in the central rapidity region, is seen to scale as \sim (N_part)^alpha, where N_part$ is the number of participating nucleons, which we have approximated as 2A for central collisions of identical nuclei. We argue that the deviation of α(\simeq…
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. It uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme, as well as the development of hadron cascades after hadronization. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densities of partons, pre-hadronic parton clusters, and final-state hadrons…
Kinetic theory is used to check the applicability of parton cascade in 1 dimensional expansion. Using the information provided by 3 dimensional parton cascade, we model the transverse expansion by an effective area. With this model, kinetic theory is able to give prediction of the time development of transverse energy which is in good agreement with the parton cascade results.
In view of the recent WA98 data of $π^0$ spectra from central Pb+Pb collisions at the CERN SPS, we analyze the production of neutral pions for A+A collisions across the periodic table at $\sqrt{s}=17$ AGeV and 200 AGeV within the framework of the parton-cascade model for relativistic heavy ion collisions. The multiplicity of the pions (having $p_T > 0.5$ GeV) in the central rapidity region, is seen to scale as $\sim (N_{part})^α$, where $N_{part}$ is the number of participating nucleons, which we have approximated as 2A for central collisions of identical nuclei. We argue that the deviation of…
We study the production of bottom quarks in $pp$ collisions at Large Hadron Collider energies using previously developed parton cascade model to explore the impact of Landau Pomeranchuk Midgal (LPM) effect on their dynamics. In contrast to the case for charm quarks reported recently, we find only a marginal impact of the suppression of multiple scatterings of partons due to the LPM effect on their production. It is felt that this happens as they are only produced in very hard collisions.
Electric conductivity is sensitive to effective cross sections among the particles of the partonic medium. We investigate the electric conductivity of a hot plasma of quarks and gluons, solving the relativistic Boltzmann equation. In order to extract this transport coefficient, we employ the Green-Kubo formalism and, independently, a method motivated by the classical definition of electric conductivity. To this end we evaluate the static electric diffusion current upon the influence of an electric field. Both methods give identical results. For the first time, we obtain numerically the Drude e…
We investigate the radiative break-up of a highly energetic quark or gluon in a high-temperature QCD plasma. Within an inertial range of momenta $T \ll ω\ll E$, where $E$ denotes the energy of the original hard parton (jet) and $T$ the temperature of of the medium, we find that, as a result of the turbulent nature of the underlying parton cascade, the quark to gluon ratio of the soft fragments tends to a universal constant value that is independent of the initial conditions. We discuss implications of this result to jet quenching physics and the problem of thermalization of the quark-gluon pla…
The high density of scattered partons predicted in nuclear collisions at very high energy makes color screening effects significant. We explain how these screening mechanisms may suppress nonperturbative, soft QCD processes, permitting a consistent calculation of quark-gluon plasma formation within the framework of perturbative QCD. We present results of a model calculation of these effects including predictions for the initial thermalized state for heavy nuclei colliding at RHIC and LHC.
We briefly recall the tremendous strides in the studies of the parton cascade model made by Klaus Geiger. Next, we argue that photons may provide confirmation of several of these ideas. Thus we know that, copious internetted partonic cascades may develop in the wake of relativistic collisions of nuclei at CERN SPS and BNL RHIC energies, We use the parton cascade model to estimate the emission of single photons generated from such cascades due to the branching of quarks $q \to q γ$, scattering of quarks and gluons, and annihilation of quarks. The formation of a hot and dense partonic matter is …
We have updated the parton and hadron cascade model PACIAE 2.0 for relativistic nuclear collisions (cf. Comput. Phys. Comm. 183(2012)333) to the new issue of PACIAE 2.1. The PACIAE model is based on PYTHIA. In the PYTHIA model, once the generated particle/parton transverse momentum $p_T$ is randomly selected, its component of $[p_x,p_y]$ was originally put on the circle with radius $p_T$ randomly. It is now replaced by put on the circumference of ellipse with half major and minor axes of $p_T(1+δ_p)$ and $p_T(1-δ_p)$, respectively, in order to investigate better the transverse momentum anisotr…
We discuss the dynamics of parton cascades that develop in dense QCD matter, and contrast their properties with those of similar cascades of gluon radiation in vacuum. We argue that such cascades belong to two distinct classes that are characterized respectively by an increasing or a constant (or decreasing) branching rate along the cascade. In the former class, of which the BDMPS, medium-induced, cascade constitutes a typical example, it takes a finite time to transport a finite amount of energy to very soft quanta, while this time is essentially infinite in the latter case, to which the DGLA…
Different treatments for the inclusion of higher-order perturbative QCD corrections in parton based transport models of relativistic heavy-ion collisions are studied and their influence on experimental observables is investigated. At RHIC, particle multiplicities may vary by more than 30%, depending on the correction scheme. A detailed analysis of the squared relative momentum transfers to be expected in parton (re)scatterings at RHIC casts doubt on the applicability of pQCD based transport approaches at the SPS and rules out the application of higher-order correction schemes based on a rescal…
The parton and hadron cascade model PACIAE 2.1 (cf. Comput. Phys. Commun.184 (2013) 1476) has been upgraded to the new issue of PACIAE 2.2. By this new issue the lepton-nucleon and lepton-nucleus (inclusive) deep inelastic scatterings can also be investigated. As an example, the PACIAE 2.2 model is enabled to calculate the specific charged hadron multiplicity in the $e^-$+p and $e^-$+D semi-inclusive deep-inelastic scattering at 27.6 GeV electron beam energy. The calculated results are well comparing with the corresponding HERMES data. Additionally, the effect of model parameters αand βin the …
We introduce a Monte Carlo space-time model for high-energy collisions with nuclei, involving the dynamical interplay of perturbative QCD parton production and evolution, with non-perturbative parton-cluster formation and `afterburner' cascading of formed pre-hadronic clusters plus hadron excitations. This approach allows us to trace the space-time history of parton and hadron degrees of freedom of nuclear collisions on the microscopical level of parton and hadron cascades in both position and momentum space, from the instant of nuclear overlap to the final yield of particles. In applying this…
Longitudinal broadening along $Δη$ direction on near side in two-dimensional ($Δϕ\times Δη$) di-hadron correlation distribution has been studied for central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV, within a dynamical multi-phase transport model. It was found that the longitudinal broadening is generated by a longitudinal flow induced by strong parton cascade in central Au+Au collisions, in comparison with p+p collisions at $\sqrt{s_{NN}}$ = 200 GeV. The longitudinal broadening may shed light on the information about strongly interacting partonic matter at RHIC.
We present the novel microscopic n-body dynamical transport approach PHQMD(Parton-Hadron-Quantum-Molecular-Dynamics) for the description of particle production and cluster formation in heavy-ion reactions at relativistic energies. The PHQMD extends the established PHSD (Parton-Hadron-String-Dynamics) transport approach by replacing the mean field by density dependent two body interactions in a similar way as in the Quantum Molecular Dynamics (QMD) models. This allows for the calculation of the time evolution of the n-body Wigner density and therefore for a dynamical description of clusters and…
Cascade solutions of the Boltzmann equation suffer from causality violation at large densities and/or scattering cross sections. Although the particle subdivision technique can reduce the causality violation, it alters event-by-event correlations and fluctuations and is also computationally expensive. Here we evaluate and then improve the accuracy of the ZPC parton cascade for elastic scatterings inside a box without using parton subdivision. We first test different collision schemes for the collision times and ordering time and find that the default collision scheme does not accurately descri…
Motivated by the classical picture of heat flow we construct a stationary temperature gradient in a relativistic microscopic transport model. Employing the relativistic Navier-Stokes ansatz we extract the heat conductivity κ for a massless Boltzmann gas using only binary collisions with isotropic cross sections. We compare the numerical results to analytical expressions from different theories and discuss the final results. The directly extracted value for the heat conductivity can be referred to as a literature reference within the numerical uncertainties.
There seems to be a general consensus now that a first glimpse of a QGP-like effect has become visible in the beautiful NA50 data on J/ψproduction and the `anomalous supression' phenomenon. On the other hand, it is still widely believed that the dynamics of heavy-ion collisions at CERN SPS energy is predominantly governed by soft, non-perturbative physics. This is ironic: after all, it is unlikely that a QGP could be formed if the underlying dynamics were essentyially soft, rather than that it requires intense quark-gluon production with sufficient cascade-like reinteractions which drive the m…
We present a study of three-particle correlations among a trigger particle and two associated particles in Au + Au collisions at $\sqrt{s_{NN}}$ = 200 GeV using a multi-phase transport model (AMPT) with both partonic and hadronic interactions. We found that three-particle correlation densities in different angular directions with respect to the triggered particle (`center', `cone', `deflected', `near' and `near-away') increase with the number of participants. The ratio of `deflected' to `cone' density approaches to 1.0 with the increasing of number of participants, which indicates that partoni…
We evaluate the spectra of produced particles (pions, kaons, antiprotons) from partonic cascades which may develop in the wake of heavy-ion collisions at CERN SPS energies and which may hadronize by formation of clusters which decay into hadrons. Using the experimental data obtained by NA35 and NA44 collaborations for S+S and Pb+Pb collisions, we conclude that the Monte Carlo implementation of the recently developed parton-cascade/cluster-hadronization model provides a reasonable description of the distributions of the particles produced in such collisions. While the rapidity distribution of t…
The longitudinal long-range correlations of the triangular flow event plane angles are calculated in a Boltzmann + hydrodynamics hybrid approach. The potential to disentangle different energy deposition scenarios is explored by utilizing two different transport approaches for the early non-equilibrium evolution. In the hadronic transport approach the particle production in high energy heavy ion reactions is mainly governed by string excitation and fragmentation processes which are absent in the parton cascade approach. We find that in both approaches the initial state shows a strong longitudin…
The shear viscosity of a gluon gas is calculated using the Green-Kubo relation. Time correlations of the energy-momentum tensor in thermal equilibrium are extracted from microscopic simulations using a parton cascade solving various Boltzmann collision processes. We find that the pQCD based gluon bremsstrahlung described by Gunion-Bertsch processes significantly lowers the shear viscosity by a factor of 3-8 compared to elastic scatterings. The shear viscosity scales with the coupling as 1/(alpha_s^2\log(1/alpha_s)). For a constant coupling constant the shear viscosity to entropy density ratio …
The dynamics of partonic cascades may be an important aspect for particle production in relativistic collisions of nuclei at CERN SPS and BNL RHIC energies. Within the Parton-Cascade Model, we estimate the production of single photons from such cascades due to scattering of quarks and gluons q g -> q gamma, quark-antiquark annihilation q qbar -> g gamma, or gamma gamma, and from electromagnetic brems-strahlung of quarks q -> q gamma. We find that the latter QED branching process plays the dominant role for photon production, similarly as the QCD branchings q -> q g and g -> g g play a crucial …
We calculate the production of high energy photons from Compton and annihilation processes as well as fragmentation off quarks in the parton cascade model. The multiple scattering of partons is seen to lead to a substantial production of high energy photons, which rises further when parton multiplication due to final state radiation is included. The photon yield is found to be proportional to the number of collisions among the cascading partons.
We examine Pb+Pb collisions at CERN SPS energy 158 A GeV, by employing the earlier developed and recently refined parton-cascade/cluster-hadronization model and its Monte Carlo implementation. This space-time model involves the dynamical interplay of perturbative QCD parton production and evolution, with non-perturbative parton-cluster formation and hadron production through cluster decays. Using computer simulations, we are able to follow the entwined time-evolution of parton and hadron degrees of freedom in both position and momentum space, from the instant of nuclear overlap to the final yi…
VNI is a general-purpose Monte-Carlo event-generator, which includes the simulation of lepton-lepton, lepton-hadron, lepton-nucleus, hadron-hadron, hadron-nucleus, and nucleus-nucleus collisions. On the basis of renormalization-group improved parton description and quantum-kinetic theory, it uses the real-time evolution of parton cascades in conjunction with a self-consistent hadronization scheme that is governed by the dynamics itself. The causal evolution from a specific initial state (determined by the colliding beam particles) is followed by the time-development of the phase-space densitie…
The production and thermalization of partons liberated in relativistic heavy ioncollisions is investigated within the parton cascade model. The momentum distribution of the partons near z=0 is found to become isotropic beyond about 1 fm/c after the overlap for the collision of lead nuclei at $\sqrt{s}=20 A GeV$ indicating a thermalization. At $\sqrt{s}=200 A GeV$ this is attained by about 0.5 fm/c after the complete overlap.
We develop a new 3+1 dimensional Monte Carlo cascade solving the kinetic on-shell Boltzmann equations for partons including the inelastic gg <-> ggg pQCD processes. The back reaction channel is treated -- for the first time -- fully consistently within this scheme. An extended stochastic method is used to solve the collision integral. The frame dependence and convergency are studied for a fixed tube with thermal initial conditions. The detailed numerical analysis shows that the stochastic method is fully covariant and that convergency is achieved more efficiently than within a standard geometr…
The parton rescattering effect on the charged hadron forward-backward multiplicity correlation in $pp$ collisions at $\sqrt s$=200 GeV is studied by a parton and hadron cascade model, PACIAE, based on the PYTHIA model. The calculated multiplicity and pseudorapidity distribution of the final state charged hadron are well compared with experimental data. It turned out that the final state charged hadron pseudorapidity distribution are different from the initial state charged partons. The parton rescattering effect on the charged hadron forward-backward multiplicity correlation increases with inc…
We calculate the net baryon rapidity distribution in Au+Au collisions at the Relativistic Heavy Ion Collider (RHIC) in the framework of the Parton Cascade Model (PCM). Parton rescattering and fragmentation leads to a substantial increase in the net baryon density at mid-rapidity over the density produced by initial primary parton-parton scatterings. The PCM is able to describe the measured net baryon density at RHIC.
The parton yield, (pseudo)rapidity distribution, and transverse momentum distribution in partonic matter assumed forming in the early stage of $pp$ and nucleus-nucleus collisions at RHIC energy ($\sqrt{s_{NN}}$=200 GeV) and LHC energy ($\sqrt{s_{NN}}$=5.5 TeV for nucleus-nucleus, 5.5 and/or 14 TeV for $pp$) are comparatively investigated with parton and hadron cascade model PACIAE. It turned out that the different parton and anti-parton spectra approach to be similar with reaction energy increasing from RHIC to LHC. We have argued that if the partonic matter forming in Au+Au collisions at RHIC…
We investigate the transport dynamics of partons in proton-proton collisions at the Large Hadron Collider using a Boltzmann transport approach, the parton cascade model. The calculations include semi-hard pQCD interaction of partons populating the nucleons and provide a space-time description of the collision in terms of cascading partons undergoing scatterings and fragmentations. Parton production and number of collisions rise rapidly with increase in center of mass energy of the collision. For a given center of mass energy, the number of parton interactions is seen to rise stronger than line…
