The correlation between the nuclear stopping and the scale invariant nucleon sideward flow at energies ranging from those available at the GSI heavy ion synchrotron (SIS) to those at the CERN Super Proton Synchrotron (SPS) is studied within ultrarelativistic quantum molecular dynamics (UrQMD). The universal behavior of the two experimental observables for various colliding systems and scale impact parameters are found to be highly correlated with each other. As there is no phase transition mechanism involved in the UrQMD, the correlation may be broken down by the sudden change of the bulk properties of the nuclear matter, such as the formation of quark-gluon plasma (QGP), which can be employed as a QGP phase transition signal in high-energy heavy ion collisions. Furthermore, we also point out that the appearance of a breakdown of the correlation may be a powerful tool for searching for the critical point on the QCD phase diagram.
Collective flows in heavy-ion collisions from AGS ($(2-11)A$ GeV) to SPS ($(40,158)A$ GeV) energies are investigated in a nonequilibrium transport model with nuclear mean-field (MF). Sideward $<p_x>$, directed $v_1$, and elliptic flows $v_2$ are systematically studied with different assumptions on the nuclear equation of state (EOS). We find that momentum dependence in the nuclear MF is important for the understanding of the proton collective flows at AGS and SPS energies. Calculated results with momentum dependent MF qualitatively reproduce the experimental data of proton sideward, directed, …
We analyze the baryon sideward and elliptic flow from SIS (0.25 $\sim$ 2 A GeV) to AGS (2 $\sim 11.0A$GeV) energies for Au + Au collisions in the relativistic transport model RBUU that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher mass continuum. There are two factors which dominantly determine the baryon flow at these energies: the momentum dependence of the scalar and vector potentials and the resonance-string degrees of freedom. We fix the explicit momentum dependence of the nucleon-meson couplings within the NL3 parameter set by th…
We study the proton sideward and elliptic differential flow for Au+Au collisions at AGS energies (2 -- 8 A cdot GeV) in a microscopic relativistic transport model that includes all baryon resonances up to a mass of 2 GeV as well as string degrees of freedom for the higher hadronic excitations. In order to explore the sensitivity of the various differential flows to the nuclear equation of state (EoS) we use three different parameterizations of the scalar- and vector mean-fields, i.e. NL2 (soft), NL23 (medium) and NL3 (hard), with their momentum dependence fitted to the experimental Schrodinger…
Nuclear stopping in the heavy ion collisions over a beam energy range from SIS, AGS up to SPS is studied in the framework of the modified UrQMD transport model, in which mean field potentials of both formed and "pre-formed" hadrons (from string fragmentation) and medium modified nucleon-nucleon elastic cross sections are considered. It is found that the nuclear stopping is influenced by both the stiffness of the equation of state and the medium modifications of nucleon-nucleon cross sections at SIS energies. At the high SPS energies, the two-bump structure is shown in the experimental rapidity…
The transverse momentum distribution of produced charged particles is investigated for gold-gold collisions at $\sqrt{s_{NN}}=200$ GeV. A simple parameterization is suggested for the particle distribution based on the nuclear stopping effect. The model can fit very well both the transverse momentum distributions at different pseudo-rapidities and the pseudo-rapidity distributions at different centralities. The ratio of rapidity distributions for peripheral and central collisions is calculated and compared with the data.
Based on the relativistic transport model ART with the hadronic equation of state extended to have a phase transition via the use of the MIT bag model, properties of phase transition of dense nuclear matter formed in relativistic heavy-ion collisions are investigated. Proton sideward and directed flows are calculated with different equation of states in Au + Au collisions at beam energies of 2, 4, 6 and 8 GeV/nucleon. Compared with AGS experimental data in existence, the boundary of first-order phase transition is roughly confined, i.e., in the range of 2.5-4 times saturation density with temp…
Nuclear stopping in heavy ion collisions (HIC) has been studied by means of rapidity distribution and asymmetry of nucleon momentum distribution. It is an important quantity in determining the outcome of a reaction. Fen Fu {\it et al.,} \cite{2} calculate both the radial flow and the degree of nuclear stopping in Pb + Pb and Ni + Ni at 0.4, 0.8 and 1.2 GeV/neucleon. They found that the expansion velocity as well as the degree of nuclear stopping are higher in the heavier system at all energies.
The detailed analysis of wide excitation function of nuclear stopping has been studied within a transport model, Isospin-dependent Quantum Molecular Dynamics model (IQMD) and an overall good agreement with the INDRA and FOPI experimental data has been achieved. It is found that mean value of isotropy in central Heavy-Ion Collision (HIC) reaches a minimum near Fermi energy and approaches a maximum around 300 - 400$A$ MeV. This suggests that, in statistical average, the equilibration is far from being reached even in central HIC especially near Fermi energy. A hierarchy in stopping of fragments,…
It is argued that the experimentally observed baryon stopping may indicate (within the present experimental uncertainties) a non-monotonous behaviour as a function of the incident energy of colliding nuclei. This can be quantified by a midrapidity reduced curvature of the net-proton rapidity spectrum. The above non-monotonous behaviour reveals itself as a "zig-zag" irregularity in the excitation function of this curvature. The three-fluid dynamic calculations with a hadronic equation of state (EoS) fail to reproduce this irregularity. At the same time, the same calculations with an EoS involvi…
We investigate stopping and baryon transport in central relativistic Pb + Pb and Au + Au collisions. At energies reached at the CERN Super Proton Synchrotron [sqrt(s_NN) = 6.3-17.3 GeV] and at RHIC (62.4 GeV), we determine the fragmentation-peak positions from the data. The resulting linear growth of the peak positions with beam rapidity is in agreement with our results from a QCD-based approach that accounts for gluon saturation. No discontinuities in the net-proton fragmentation peak positions occur in the expected transition region from partons to hadrons at 6-10 GeV.
We study the radiative energy loss contribution to proton stopping in $AA$ collisions. The analyses is performed within the light-cone path integral approach to induced gluon emission. We have found that the radiative correction can fill in partly the midrapidity dip in the net proton rapidity distribution in $AA$ collisions at $\sqrt{s}\sim 10$ GeV. We argue that at $\sqrt{s}\sim 10$ GeV the net proton fluctuations at midrapidity may be dominated by the initial fluctuations of the proton flow, which, to a good accuracy, should be binomial.
A systematic study of the in-medium correction factor ($F$) on nucleon-nucleon elastic cross section is performed within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The effects of the beam energy dependence of $F$ on the directed, elliptic flow and nuclear stopping in $^{197}$Au+$^{197}$Au collisions with energy ranging from $0.09$ to $0.8A$ GeV are explored. It is found that the directed, elliptic flow and nuclear stopping at relatively low energies are very sensitive to $F$, and the sensitivity gradually weakens with increasing beam energy. The beam energy dependent in-m…
The nuclear equation of state (EoS) is investigated by flow phenomena in relativistic heavy-ion collisions, both in transverse and radial direction, in comparison to experimental data from 150 A MeV to 11 A GeV. To this aim the collective dynamics of the nucleus-nucleus collision is described within a transport model of the coupled channel RBUU type. There are two factors which dominantly determine the baryon flow at these energies: the momentum dependence of the scalar ($U_S$) and vector potentials ($U_μ$) for baryons and the resonance/string degrees of freedom for energetic hadron excitation…
Using a relativistic transport (ART) model, we study the stopping power, the formation of superdense hadronic matter as well as the strength of transverse and radial flow in central Au+Au collisions at beam momentum from 2 to 12 GeV/c per nucleon. We find that complete stopping is achieved in the whole beam momentum range. In particular, the proton rapidity distribution scaled by the beam rapidity is independent of the beam momentum, and this is in agreement with the experimental findings. Also, a large volume of superdense hadronic matter with a local energy density exceeding that expected fo…
Proton Collectivity in Au+Au Collisions at $\sqrt{s_{\rm NN}}=2.4-4.5$~GeV from a Unified Purely Hadronic EOS without QCD Phase Transition
School of Physics and Electronic Science, Guizhou Normal University（贵州师范大学物理与电子科学学院）；Guizhou Provincial Key Laboratory of Radio Astronomy and Data Processing, Guizhou Normal University（贵州师范大学贵州省射电天文与数据处理重点实验室）；Department of Physics, Tsinghua University（清华大学物理系）；Center for High Energy Physics, Tsinghua University（清华大学高能物理中心）
It is argued that an irregularity in the baryon stopping is a natural consequence of a phase transition occurring in the compression stage of a nuclear collision. It is a combined effect of the softest point inherent in an equation of state (EoS) with a phase transition and a change in the nonequilibrium dynamics from hadronic to partonic transport. Thus, this irregularity is a signal from a hot and dense stage of the nuclear collision. In order to illustrate this proposition, calculations within the three-fluid model were performed with three different EoS's: a purely hadronic EoS, an EoS wit…
Simulations of relativistic heavy-ion collisions within the three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS involving deconfinement transition are presented. The latter are an EoS with the first-order phase transition and that with a smooth crossover transition. The model setup is described in detail. The analysis is performed in a wide range of incident energies 2.7 GeV $< \sqrt{s_{NN}} <$ 39 GeV in terms of the center-of-mass energy. Results on proton and net-proton rapidity distributions are reported. Comparison with available data indicate …
The beam energy dependence of the directed flow is a sensitive probe for the properties of strongly interacting matter. We consider different implementations of momentum-dependent hadronic mean fields in the relativistic quantum molecular dynamics (RQMD) framework. First, Lorentz scalar implementation of a Skyrme type potential is examined. Then, full implementation of the Skyrme type potential as a Lorentz vector in the RQMD approach is proposed. We find that scalar implementation of the Skyrme force is too weak to generate repulsion explaining observed data of sideward flows at $\sqrt{s_{NN}…
The stopping of baryons in heavy ion collisions at beam momenta of $p_{\rm lab} = 20-160A$ GeV is lacking a quantitative description within theoretical calculations. Heavy ion reactions at these energies are experimentally explored at the Super Proton Synchrotron (SPS) and the Relativistic Heavy Ion Collider (RHIC) and will be studied at future facilities such as FAIR and NICA. Since the net baryon density is determined by the amount of stopping, this is the pre-requisiste for any investigation of other observables related to structures in the QCD phase diagram such as a first-order phase tran…
The derivation of information useful for understanding the physics inside compact stars from HIC observations is a difficult task. Complications due to finite size, different chemistry, non-adiabatic compression, incomplete stopping and structural effects must be overcome. This can only be convincingly achieved by a successful simulation of many experimental observables varying incident energy, system size and isospin content. Using now available systematic FOPI data in the SIS energy range we try to trace the path to take.
We investigate possible effects of correlations between stopped nucleons on higher order proton cumulants at low energy heavy-ion collisions. We find that fluctuations of the number of wounded nucleons $N_{\mathrm{part}}$ lead to rather nontrivial dependence of the correlations on the centrality; however, this effect is too small to explain the large and positive four-proton correlations found in the preliminary data collected by the STAR collaboration at $\sqrt{s}=7.7$ GeV. We further demonstrate that, by taking into account additional proton clustering, we are able to qualitatively reproduce…
We present blast wave fits to elliptic flow ($v_{2}(p_{\rm T})$) data in minimum bias collisions from the $\sqrt{s_{\rm NN}} =$ 7.7--200 GeV at RHIC, and 2.76 TeV at LHC. The fits are performed separately for particles and corresponding anti-particles. The mean transverse velocity parameter $β$ shows an energy dependent difference between particles and corresponding anti-particles, which increases as the beam energy decreases. Possible effects of feed down, baryon stopping, anti-particle absorption, and early production times for anti-particles are discussed.
The features of net baryon productions and collective flow in relativistic heavy-ion collisions at energies reached at the CERN Large Hadron Collider (LHC), BNL Relativistic Heavy Ion Collider (RHIC), CERN Super Proton Synchrotron (SPS) and BNL Alternating Gradient Synchrotron (AGS) with the model of Non-Uniform Flow Model(NUFM) are systematically studied in this paper. Especially we predict the feature of net baryon productions and collective flow at LHC $\sqrt{s_{NN}}$=5500 GeV basing on the detailed study of that at RHIC $\sqrt{s_{NN}}$=62.4 and 200GeV. The dependencies of the features of b…
Analysis of elliptic flow of protons and antiprotons in Au+Au collisions is performed in a wide range of incident energies $\sqrt{s_{NN}}$ = 7.7--62.4 GeV. Simulations has been done within the three-fluid model employing a purely hadronic equation of state (EoS) and two versions of the EoS involving deconfinement transition: an EoS with the first-order phase transition and that with a smooth crossover transition. It is found that the proton data are reproduced approximately to the same extent within all of the scenarios, including the hadronic one, while the deconfinement scenarios look certai…
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…
The ring structures that appear in Au+Au collisions at collision energies $\sqrt{s_{NN}}=$ 3 -- 30 GeV are studied. The calculations are performed within the model of three-fluid dynamics. It is demonstrated that a pare of vortex rings are formed, one at forward and another at backward rapidities, in ultra-central Au+Au collisions at $\sqrt{s_{NN}}>$ 4 GeV. The vortex rings carry information about early stage of the collision, in particular about the stopping of baryons. It is shown that these rings can be detected by measuring the ring observable $R_Λ$ even in rapidity range $0<y<0.5$ (or $-0…
We present UrQMD predictions for the comparison of the recently measured Ag+Ag and Au+Au runs at a beam energy of $E_\mathrm{lab}$ = 1.23~$A$GeV explored by the HADES experiment. To this aim, different centrality definitions are investigated: We suggest that in the case of particle production, both systems should be compared at the same number of participating nucleons, while for a comparison of the (elliptic) flow, a selection on the initial state eccentricity - as in high energy reaction - is better suited. Generally, we find good agreement between both system, if these centrality criteria a…
We perform a systematic study of elliptic flow ($v_2$) in Au+Au collision at $\sqrt{s_{NN}}=5$ GeV by using a microscopic transport model JAM. The centrality, pseudorapidity, transverse momentum and beam energy dependence of $v_2$ for charged as well as identified hadrons are studied. We investigate the effects of both the hadronic mean-field and the softening of equation of state (EoS) on elliptic flow. The softening of EoS is realized by imposing attractive orbits in two body scattering, which can reduce the pressure of the system. We found that the softening of EoS leads to the enhancement …
This work presents a three-dimensional dynamical initialization model for relativistic heavy-ion collisions, implementing local energy-momentum conservation and baryon charge fluctuations at string junctions. Constraining parameters using experimental data from p+p collisions at various collision energies, the model provides a very good description of the charged hadron and net proton rapidity distributions in Au+Au collisions from 7.7 to 200 GeV and Pb+Pb collisions at 8.77 and 17.3 GeV. We demonstrate the importance of fluctuations of baryon densities to string junctions for describing net-p…
Collective transverse flow in heavy-ion collisions at incident energies E_{lab} = (1 -160)A GeV is analyzed within the model of 3-fluid dynamics (3FD). Simulations are performed with purely hadronic equation of state (EoS). At the AGS energies the flow turns out to be sensitive to the stopping power of nuclear matter rather than only to the stiffness of the EoS. When the stopping power is fixed to reproduce other observables, the flow data favor more and more soft EoS with the incident energy rise, which can be associated with ``a transition from hadronic to string matter'' reported in the Had…
Predictions of baryon directed flow in heavy-ion collisions at high baryon density
Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research（鲍里索夫理论物理实验室，核联合研究所）；National Research Center ”Kurchatov Institute”（库尔恰托夫国家研究中心）
We discuss systematic uncertainties in the chemical freeze-out parameters from the $χ^2$ analysis of hadron multiplicity ratios in the heavy-ion collision experiments. The systematics due to the choice of specific hadron ratios are found to lie within the experimental uncertainties. The variations obtained by removing the usual constraints on the conserved charges show similar behavior. The net charge to net baryon ratios in such unconstrained systems are commensurate with the expected value obtained from the protons and neutrons of the colliding nuclei up to the center of mass energies $\sim …
The higher order moments of the net-baryon distributions in relativistic heavy ion collisions are useful probes for the QCD critical point and fluctuations. Within a simple model we study the colliding energy and centrality dependence of the net-proton distributions in the central rapidity region. The model is based on considering the baryon stopping and pair production effects in the processes. Based on some physical reasoning, the dependence is parameterized. Predictions for the net-proton distributions for Au+Au and Pb+Pb collisions at different centralities at $\sqrt{s_{NN}}$=39 and 2760 G…
In ultra-relativistic heavy ion collisions at $\roots\approx200$ GeV, the azimuthal emission anisotropy of hadrons with low and intermediate transverse momentum ($p_T\lesssim 4$ GeV/c) displays an intriguing scaling. In particular, the baryon (meson) emission patterns are consistent with a scenario in which a bulk medium of flowing quarks coalesces into three-quark (two-quark) "bags." While a full understanding of this number of constituent quark (NCQ) scaling remains elusive, it is suggestive of a thermalized bulk system characterized by colored dynamical degrees of freedom-- a quark-gluon pl…
We present a new event generator based on the three-fluid hydrodynamics approach for the early stage of the collision, followed by a particlization at the hydrodynamic decoupling surface to join to a microscopic transport model, UrQMD, to account for hadronic final state interactions. We present first results for nuclear collisions of the FAIR/NICA energy scan program (Au+Au collisions, $\sqrt{s_{NN}}=4-11$ GeV). We address the directed flow of protons and pions as well as the proton rapidity distribution for two model EoS, one with a first order phase transition the other with a crossover typ…
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…
A two phase cascade is presented for the treatment of ultra-high energy ion-ion collisions at energies from 17-200 GeV. First a high energy, fast cascade is performed, in which original baryons and freed hard partons, if any, collide. This stage ignores energy loss from soft (slow) processes. In this first version no hard processes, aside from Drell-Yan production, are included. The space-time history of the hard phase is then used as input to reconstruct soft energy-loss, which occurs over a longer time scale. Soft meson production is therefore treated as coherent over groups of interacting n…
The recent net-proton fluctuation results of the STAR (Solenoidal Tracker At RHIC) experiment from beam energy scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC) have drawn much attention to exploring the QCD critical point and the nature of deconfinement phase transition. There has been much speculation that the non-monotonic behavior of $κσ^{2}$ of the produced protons around $\sqrt{s_{\rm NN}}$ = 19.6 GeV in the STAR results may be due to the existence of QCD critical point. However, the experimentally measured proton distributions contain protons from heavy resonance deca…
Excitation function for global Λpolarization in relativistic heavy ion collisions with the Core Corona model
Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México（墨西哥国立自治大学核科学研究所）；Facultad de Ciencias Físico-Matemáticas, Universidad Autónoma de Sinaloa（西阿拉索阿自治大学物理数学科学学院）；Facultad de Ciencias-CUICBAS, Universidad de Colima（科利马大学理学院-CUICBAS）
