Ultrarelativistic Quantum Molecular Dynamics Research Articles

Elliptic flow splitting between protons and antiprotons from hadronic potentials

The difference in elliptic flow between protons and antiprotons, produced in [Formula: see text] collisions at center-of-mass energies [Formula: see text], is studied within a modified version of the ultra-relativistic quantum molecular dynamics (UrQMD) model. Two different model scenarios are compared: the cascade mode and the mean field mode which includes potential interactions for both formed and pre-formed hadrons. The model results for the elliptic flow of protons and the relative elliptic flow difference between protons and antiprotons obtained from the mean field mode agree with the available experimental data, while the elliptic flow difference is near zero for the cascade mode. Our results show that the elliptic flow splitting, observed for particles and antiparticles, can be explained by the inclusion of proper hadronic interactions. In addition, the difference in elliptic flow between protons and antiprotons depends on the centrality and the rapidity window. With smaller centrality and/or rapidity acceptance, the observed elliptic flow splitting is more sensitive to the beam energy, indicating a strong net baryon density dependence of the effect. We propose to confirm this splitting at the upcoming experiments from Beam Energy Scan (BES) Phase-II at Relativistic Heavy Ion Collider (RHIC), the Compressed Baryonic Matter (CBM) at Facility for Antiproton and Ion Research (FAIR), High Intensity heavy ion Accelerator Facility (HIAF) and Nuclotron-based Ion Collider fAcility (NICA).

Study of diffusion coefficients of identified particles at energies available at BNL Relativistic Heavy Ion Collider

Using event-by-event fluctuations, we study the diffusion parameters of net-charge, net-pion, net-kaon, and net-proton in the heavy-ion jet interaction generator (HIJING), and ultra-relativistic quantum molecular dynamics (UrQMD) models at different collision energies \sqsn available at BNL Relativistic Heavy Ion Collider (RHIC). The diffusion parameter ($\sigma$) of net-charge and identified particles are estimated in rapidity space at various \sqsn. It is observed that, the $\sigma$ values are independent of collision energies but emphasises the particle-species dependence of diffusion coefficient in the QGP medium. The present work on particle-species dependence of diffusion coefficient provides a baseline for comparison with the experimental data.

Beam energy dependence of net- Λ fluctuations measured by the STAR experiment at the BNL Relativistic Heavy Ion Collider

The measurements of particle multiplicity distributions have generated considerable interest in understanding the fluctuations of conserved quantum numbers in the Quantum Chromodynamics (QCD) hadronization regime, in particular near a possible critical point and near the chemical freeze-out. We report the measurement of efficiency and centrality bin width corrected cumulant ratios ($C_{2}/C_{1}$, $C_{3}/C_{2}$) of net-$\Lambda$ distributions, in the context of both strangeness and baryon number conservation, as a function of collision energy, centrality and rapidity. The results are for Au + Au collisions at five beam energies ($\sqrt{s_{NN}}$ = 19.6, 27, 39, 62.4 and 200 GeV) recorded with the Solenoidal Tracker at RHIC (STAR). We compare our results to the Poisson and negative binomial (NBD) expectations, as well as to Ultra-relativistic Quantum Molecular Dynamics (UrQMD) and Hadron Resonance Gas (HRG) model predictions. Both NBD and Poisson baselines agree with data within the statistical and systematic uncertainties. The ratios of the measured cumulants show no features of critical fluctuations. The chemical freeze-out temperatures extracted from a recent HRG calculation, which was successfully used to describe the net-proton, net-kaon and net-charge data, indicate $\Lambda$ freeze-out conditions similar to those of kaons. However, large deviations are found when comparing to temperatures obtained from net-proton fluctuations. The net-$\Lambda$ cumulants show a weak, but finite, dependence on the rapidity coverage in the acceptance of the detector, which can be attributed to quantum number conservation.

Event-by-event fluctuations of maximum particle density with respect to the width of the pseudo-rapidity interval at a few A GeV/c

A detailed study of event-by-event fluctuations of maximum particle density of the produced particles with respect to the width of the pseudo-rapidity interval in terms of the scaled variance ω has been carried out for 16O-AgBr, 28Si-AgBr and 32S-AgBr interactions at 4.5 A GeV/c. For all the interactions the values of scaled variance are found to be greater than one indicating the presence of strong event-by-event fluctuations of maximum particle density values in the multiparticle production process. The event-by-event fluctuations are found to decrease with the increase of the width of the pseudo-rapidity interval. Experimental analysis has been compared with the results obtained from the analysis of events simulated by generating random numbers (MC-RAND) and the Ultra-Relativistic Quantum Molecular Dynamics (UrQMD) model. MC-RAND events show significantly less event-by-event fluctuations in comparison to the experimental data. The UrQMD model also failed to reproduce the experimental results. Comparison of our analysis with the outcome of other analysed emulsion data has also been presented.

Vorticity in low-energy heavy-ion collisions

We study the kinematic and thermal vorticities in low-energy heavy-ion collisions by using the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. We explore their time evolution and spatial distribution. We find that the initial vorticities have a non-monotonic dependence on the collision energy $\sqrt{s_{\rm NN}}$: as $\sqrt{s_{\rm NN}}$ grows the vorticities first increase steeply and then decrease with the turning point around $\sqrt{s_{\rm NN}}\sim 3-5$ GeV depending on the centrality.

Progress of quantum molecular dynamics model and its applications in heavy ion collisions

In this review article, we first briefly introduce the transport theory and quantum molecular dynamics model applied in the study of the heavy ion collisions from low to intermediate energies. The developments of improved quantum molecular dynamics model (ImQMD) and ultra-relativistic quantum molecular dynamics model (UrQMD), are reviewed. The reaction mechanism and phenomena related to the fusion, multinucleon transfer, fragmentation, collective flow and particle production are reviewed and discussed within the framework of the two models. The constraints on the isospin asymmetric nuclear equation of state and in-medium nucleon-nucleon cross sections by comparing the heavy ion collision data with transport models calculations in last decades are also discussed, and the uncertainties of these constraints are analyzed as well. Finally, we discuss the future direction of the development of the transport models for improving the understanding of the reaction mechanism, the descriptions of various observables, the constraint on the nuclear equation of state, as well as for the constraint on in-medium nucleon-nucleon cross sections.

Nucleon effective mass splitting and density-dependent symmetry energy effects on elliptic flow in heavy ion collisions at Elab= 0.09 ~ 1.5 GeV/nucleon * * Supported in part by the National Natural Science Foundation of China (11875125, 11947410, 11847315, 11505057); the Zhejiang Provincial Natural Science Foundation of China (LY18A050002, LY19A050001) and the Ten Thousand Talent Program of Zhejiang province (2018R52017)

By incorporating an isospin-dependent form of the momentum-dependent potential in the ultra-relativistic quantum molecular dynamics (UrQMD) model, we systematically investigate effects of the neutron-proton effective mass splitting = and the density-dependent nuclear symmetry energy on the elliptic flow in + collisions at beam energies from 0.09 to 1.5 GeV/nucleon. It is found that at higher beam energies ( 0.25 GeV nucleon) with the approximately 75 MeV difference in slopes of the two different , and the variation of ranging from –0.03 to 0.03 at saturation density with isospin asymmetry , the has a stronger influence on the difference in between neutrons and protons, i.e., , than has. Meanwhile, at lower beam energies ( 0.25 GeV nucleon), is sensitive to both the and the . Moreover, the influence of on is more evident with the parameters of this study when using the soft, rather than stiff, symmetry energy.

Application of microscopic transport model in the study of nuclear equation of state from heavy ion collisions at intermediate energies

The equation of state (EOS) of nuclear matter, i.e., the thermodynamic relationship between the binding energy per nucleon, temperature, density, as well as the isospin asymmetry, has been a hot topic in nuclear physics and astrophysics for a long time. The knowledge of the nuclear EOS is essential for studying the properties of nuclei, the structure of neutron stars, the dynamics of heavy ion collision (HIC), as well as neutron star mergers. HIC offers a unique way to create nuclear matter with high density and isospin asymmetry in terrestrial laboratory, but the formed dense nuclear matter exists only for a very short period, one cannot measure the nuclear EOS directly in experiments. Practically, transport models which often incorporate phenomenological potentials as an input are utilized to deduce the EOS from the comparison with the observables measured in laboratory. The ultrarelativistic quantum molecular dynamics (UrQMD) model has been widely employed for investigating HIC from the Fermi energy (40 MeV per nucleon) up to the CERN Large Hadron Collider energies (TeV). With further improvement in the nuclear mean-field potential term, the collision term, and the cluster recognition term of the UrQMD model, the newly measured collective flow and nuclear stopping data of light charged particles by the FOPI Collaboration can be reproduced. In this article we highlight our recent results on the studies of the nuclear EOS and the nuclear symmetry energy with the UrQMD model. New opportunities and challenges in the extraction of the nuclear EOS from transport models and HIC experiments are discussed.

Beam energy dependence of cumulants of the net-baryon, net-charge, and deuteron multiplicity distributions in Au + Au collisions at sNN=3.0–5.0 GeV

Within the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Lorentz-covariant treatment of nuclear mean-field potential is considered, the fluctuations of net-baryon, net-charge and deuterons multiplicity distributions in Au+Au head-on collisions at $\sqrt{s_{NN}}=3.0-5.0$ GeV are calculated. The results show that the nuclear mean-field potential can significantly enhance the magnitude of baryon number fluctuations in narrow rapidity windows, and this enhancement rapidly weakens with increasing beam energy. However, for proton and net-charge number fluctuations, the mean-field effects are less noticeable than that for baryon number. In addition, for net-charge number fluctuations, the negative binomial distribution agrees well with the calculated results at mid-pseudorapidity window. Finally, the event-by-event fluctuations of deuteron number in the coalescence production picture are calculated as well, it is found that its cumulant ratios decrease linearly with increasing the average multiplicity of deuterons per event, i.e., increase with increasing beam energy.

Effects of impact parameter filters on observables in heavy-ion collisions at INDRA energies

The collision centrality (or the impact parameter b) in heavy-ion experiments is inferred from final state observables, however, usually b is an input to theoretical calculations. The effects of different methods used for the centrality selection (i.e. total charged multiplicity Mch, total transverse kinetic energy of light charged particles , and the ratio of transverse-to-longitudinal kinetic energy ERAT) on the nuclear stopping and the collective flow are studied in Xe+Sn collisions at INDRA energies (/nucleon). The study is conducted within the framework of the ultra-relativistic quantum molecular dynamics (UrQMD) model. It is found that the nuclear stopping power RE obtained from events binning with ERAT is larger than the experimental data as well as the results obtained using Mch and . At Ebeam = 50 MeV/nucleon, the elliptic flow from events selected with different methods spreads widely, especially for more central collisions. The elliptic flow from events sorted by ERAT is weakly dependent on the collision centrality. The difference in elliptic flow at mid-rapidity among different centrality filters steadily decreases with increasing beam energy and impact parameter. At 150 MeV/nucleon, the differences in directed and elliptic flows arising from different centrality filters vanish.

Study of the nuclear symmetry energy from the rapidity-dependent elliptic flow in heavy-ion collisions around 1 GeV/nucleon regime

The elliptic flow ratio of neutrons versus protons in heavy-ion collisions (HICs) is one of the important probes to constrain the nuclear symmetry energy, however measuring the flow of neutrons with high precision is a great challenge for experimental techniques. In this work, the elliptic flow of protons is studied and it is found that the rapidity at which the sign of v2 changes from negative to positive is sensitive to the density dependence of the symmetry energy. By comparing the existing FOPI experimental data for proton flows to the calculations with the ultrarelativistic quantum molecular dynamics (UrQMD) model, the slope parameter of the nuclear symmetry energy is extracted to be L0=43±20 MeV at 95% confidence level. This is in good agreement with many recent results from investigations of nuclear structure properties and also partly overlaps with the recent result of the ASY-EOS experiment.

Fluctuations of identified particle yields using the νdyn variable at energies available at the BNL Relativistic Heavy Ion Collider

We study the fluctuations of net-charge, net-pion, net-kaon and net-proton using $D$-measure and $\nu_{dyn}$ variables in heavy-ion jet interaction generator (HIJING), ultra-relativistic quantum molecular dynamics (UrQMD), and hadron resonance gas (HRG) model at different collision energies \sqsn. It has been observed that, the values of $D$ strongly dependent on $\Delta \eta$ in HIJING and UrQMD models and independent in HRG model. The diffusion coefficients ($\sigma$) of identified particles are estimated at various \sqsn. It is observed that, the $\sigma$ values are independent of collision energies but emphasizes the particle species dependence of diffusion coefficient in the QGP medium. This study provides a realistic baseline for comparison with the experimental data.

Centrality Dependence of Multiplicity Fluctuations in Ion-Ion Collisions from the Beam Energy Scan at FAIR

Multiplicity distributions and event-by-event multiplicity fluctuations in AuAu collisions at energies in future heavy-ion experiment at the Facility for Anti-proton and Ion Research (FAIR) are investigated. Events corresponding to FAIR energies are simulated in the frame work of Ultra Relativistic Quantum Molecular Dynamics (URQMD) model. It is observed that the mean and the width of multiplicity distributions monotonically increase with beam energy. The trend of variations of dispersion with mean number of participating nucleons for the centrality-bin width of 5% are in accord with the Central Limit Theorem. The multiplicity distributions in various centrality bins as well as for full event samples are observed to obey Koba, Nielsen and Olesen (KNO) scaling. The trends of variations of scaled variance with beam energy are also found to support the KNO scaling predictions for larger collision centrality. The findings also reveal that the statistical fluctuations in 5% centrality-bin width appear to be under control.

Backward nucleon production by heavy baryonic resonances in proton-nucleus collisions

The production of backward nucleons, $N(180^\circ)$, at $180^\circ$ in the nuclear target rest frame in proton-nucleus ($\mathrm{p}+A$) collisions is studied. The backward nucleons appearing outside of the kinematically allowed range of proton-nucleon ($\mathrm{p}+N$) reactions are shown to be due to secondary reactions of heavy baryonic resonances produced inside the nucleus. Baryonic resonances $R$ created in primary $\mathrm{p}+N$ reactions can change their masses and momenta due to successive collisions $R+N\rightarrow R +N $ with other nuclear nucleons. Two distinct mechanisms and kinematic restrictions are studied: the reaction $R+N\rightarrow N(180^\circ)+N$ and the resonance decay $R\rightarrow N(180^\circ)+\pi$. Simulations of $\mathrm{p}+A$ collisions using the Ultra-relativistic Quantum Molecular Dynamics model support these mechanisms and are consistent with available data on proton backward production.

System size dependence of net-charge fluctuation in nucleus-nucleus collisions at FAIR energies

Dynamical net-charge fluctuations are studied in symmetric nuclear collisions of different system size and at two different collision energies that in the near future will be available at the Facility for Antiproton and Ion Research (FAIR). Multiparticle emission data simulated by the ultra-relativistic quantum molecular dynamics (UrQMD) are analyzed for this purpose. Our primary objective is to examine the system size dependence of dynamical fluctuation of conserved charge at typical FAIR conditions. The centrality, pseudorapidity interval size and azimuthal angle interval size dependence of the dynamical fluctuations are studied too. The effects of global charge conservation (GCC) and finite multiplicity bin width correction are taken into account. To a large extent the systematics followed by the dynamical fluctuations at FAIR conditions are found to be a lower energy extrapolation of the observations made in this regard in the Relativistic Heavy-ion Collider (RHIC) experiments.

A hadronic transport analysis on the Δ mass in Au + Au reactions at 1.23 AGeV

AbstractThis study is motivated by upcoming data from the high acceptance di‐electron spektrometer (HADES) collaboration at gesellschaft für schwerionenforschung, which presented preliminary data on a possible mass shift of the Δ(1232) resonance in central Au + Au reactions at Elab = 1.23 AGeV. This effect is explored via the Ultra Relativistic Quantum Molecular Dynamics transport model, allowing us to track down each decaying Δ(1232) resonance and check whether it can be reconstructed. The obtained results show that the apparent mass shift on the order of 50 MeV can be explained by a late‐stage formation effect and a long‐evolving Δ ↔ N + π cycle.

Anisotropic flow of charged and identified hadrons at FAIR energies and its dependence on the nuclear equation of state

In this article, we examine the equation of state (EoS) dependence of the anisotropic flow parameters ($v_{1}$, $v_{2}$ and $v_{4}$) of charged and identified hadrons, as a function of transverse momentum ($p_{\rm T}$), rapidity ($y_{c.m.}$) and the incident beam energy ($\rm E_{\rm Lab}$) in mid-central Au + Au collisions in the energy range $\rm E_{\rm Lab} = 6 -25$ A GeV. Simulations are carried out by employing different variants of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, namely the pure transport (cascade) mode and the hybrid mode. In the hybrid mode, transport calculations are coupled with the ideal hydrodynamical evolution. Within the hydrodynamic scenario, two different equations of state (EoS) viz. Hadron gas and Chiral + deconfinement EoS have been employed separately to possibly mimic the hadronic and partonic scenarios, respectively. It is observed that the flow parameters are sensitive to the onset of hydrodynamic expansion of the fireball in comparison to the pure transport approach. The results would be useful as predictions for the upcoming low energy experiments at Facility for Antiproton and Ion Research (FAIR) and Nuclotron-based Ion Collider fAcility (NICA).

Volume fluctuation and multiplicity correlation in higher-order cumulants

Initial volume fluctuation (VF) arising from the participant fluctuation would be the background which should be subtracted experimentally from the measured higher-order cumulants. We study the validity of the Volume Fluctuation Correction (VFC) on higher-order net-proton cumulants by using simple toy model and UrQMD model in Au+Au collisions at \sqrt s_{NN} = 200 GeV for various centrality definitions. The results are compared to the conventional data driven method called Centrality Bin Width Correction (CBWC). We find VFC works well in toy model assuming independent particle production (IPP), but does not seem to work well in UrQMD model. It is also found that cumulants are strongly affected by the multiplicity correlation effect as well as the centrality resolution effect. These results show that neither VFC nor CBWC are perfect method. Thus, both methods should be compared in the real experiment.

Investigations of Anisotropic Flow Using Multiparticle Azimuthal Correlations in pp, p-Pb, Xe-Xe, and Pb-Pb Collisions at the LHC.

Measurements of anisotropic flow coefficients (v_{n}) and their cross-correlations using two- and multiparticle cumulant methods are reported in collisions of pp at sqrt[s]=13 TeV, p-Pb at a center-of-mass energy per nucleon pair sqrt[s_{NN}]=5.02 TeV, Xe-Xe at sqrt[s_{NN}]=5.44 TeV, and Pb-Pb at sqrt[s_{NN}]=5.02 TeV recorded with the ALICE detector. The multiplicity dependence of v_{n} is studied in a very wide range from 20 to 3000 particles produced in the midrapidity region |η|<0.8 for the transverse momentum range 0.2<p_{T}<3.0 GeV/c. An ordering of the coefficients v_{2}>v_{3}>v_{4} is found in pp and p-Pb collisions, similar to that seen in large collision systems, while a weak v_{2} multiplicity dependence is observed relative to nucleus-nucleus collisions in the same multiplicity range. Using a novel subevent method, v_{2} measured with four-particle cumulants is found to be compatible with that from six-particle cumulants in pp and p-Pb collisions. The magnitude of the correlation between v_{n}^{2} and v_{m}^{2}, evaluated with the symmetric cumulants SC(m,n) is observed to be positive at all multiplicities for v_{2} and v_{4}, while for v_{2} and v_{3} it is negative and changes sign for multiplicities below 100, which may indicate a different v_{n} fluctuation pattern in this multiplicity range. The observed long-range multiparticle azimuthal correlations in high multiplicity pp and p-Pb collisions can neither be described by pythia 8 nor by impact-parameter-Glasma, music, and ultrarelativistic quantum molecular dynamics model calculations, and hence, provide new insights into the understanding of collective effects in small collision systems.

Delta mass shift as a thermometer of kinetic decoupling in Au + Au reactions at 1.23 AGeV

The HADES experiment at GSI will soon provide data on the production and properties of Δ(1232) baryons from Au + Au reactions at 1.23 AGeV. Using the Ultra Relativistic Quantum Molecular Dynamics model, we predict the yield and spectra of Δ(1232) resonances. In addition we show that one expects to observe a mass shift of the Δ(1232) resonance on the order of 50 MeV in the reconstructable Δ(1232) mass distribution. This mass shift can be understood in terms of late stage Δ(1232) formation with limited kinetic energy. We show how the mass shift can be used to constrain the kinetic decoupling temperature of the system.