Ultrarelativistic Quantum Molecular Dynamics Research Articles

Photon and dilepton production at the Facility for Proton and Anti-Proton Research and beam-energy scan at the Relativistic Heavy-Ion Collider using coarse-grained microscopic transport simulations

We present calculations of dilepton and photon spectra for the energy range $E_{\text{lab}}=2-35$ $A$GeV which will be available for the Compressed Baryonic Matter (CBM) experiment at the future Facility for Anti-Proton and Ion Research (FAIR). The same energy regime will also be covered by phase II of the Beam Energy Scan at the Relativistic Heavy-Ion Collider (RHIC-BES). Coarse-grained dynamics from microscopic transport calculations of the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model is used to determine temperature and chemical potentials, which allows for the use of dilepton and photon-emission rates from equilibrium quantum-field theory calculations. The results indicate that non-equilibrium effects, the presence of baryonic matter and the creation of a deconfined phase might show up in specific manners in the measurable dilepton invariant mass spectra and in the photon transverse momentum spectra. However, as the many influences are difficult to disentangle, we argue that the challenge for future measurements of electromagnetic probes will be to provide a high precision with uncertainties much lower than in previous experiments. Furthermore, a systematic study of the whole energy range covered by CBM at FAIR and RHIC-BES is necessary to discriminate between different effects, which influence the spectra, and to identify possible signatures of a phase transition.

Understanding pseudorapidity dependence of elliptic flow in heavy-ion collisions using a transport model

Author(s): Nasim, M; Esha, R; Huang, HZ | Abstract: A systematic study of the pseudorapidity dependence of elliptic flow parameter using transport models (e.g., a multiphase transport model, AMPT, and ultrarelativistic quantum molecular dynamics, UrQMD) has been presented. We have observed that while at mid-pseudorapidity the elliptic flow measured using the event-plane method differs significantly from that measured by actual reaction plane method, both the event-plane and reaction-plane methods give the same elliptic flow for far forward and backward pseudorapidity. This indicates that the magnitude of measured v2 around midrapidity strongly depends on the analysis method. Therefore, one should use the same procedure (as used in data analysis) in model calculations while comparing model results and experimental data. We find the shape of v2(η) measured by the PHOBOS experiment is not reproduced by using actual v2 (i.e., measured with respect to the reaction plane) from AMPT and UrQMD models. The shape and magnitude of measured v2(η) can be explained by the AMPT model with string-melting mode only if one uses the same procedure as used in data analysis. Magnitude of elliptic flow can be reproduced for all pseudorapidity range by taking the parton-parton interaction cross section to be 3 mb at sNN=62.4 and 200 GeV. This implies that the partonic interactions are necessary to reproduce data at sNN=62.4 and 200 GeV and the strength of partonic interactions at far forward and backward rapidity is as strong as at midrapidity. Both UrQMD and AMPT with default mode fail to explain the data.

Multifractal detrended moving average analysis of particle density functions in relativistic nuclear collisions

Fluctuations in particle density functions in 28Si+Ag(Br) collision at 14.5A GeV and 32S+Ag(Br) collision at 200A GeV are investigated using the multifractal detrended moving average (MFDMA) method. Multifractal parameters obtained from the data analysis are systematically compared with the ultra-relativistic quantum molecular dynamics (UrQMD) model simulation. It is found that the single particle density functions in both the experiments are multifractal in nature. Further, the degree of multifractality in the simulated event samples is almost equal to the corresponding empirical data. The results of this analysis differ significantly from those obtained from other conventional techniques of multifractal analysis previously used for the same sets of data.

Equilibration of hadrons in HICs via Hagedorn States

Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition region between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). These states are believed to appear near the Hagedorn temperature TH which in our understanding equals the critical temperature Tc. A covariantly formulated bootstrap equation is solved to generate the zoo of these particles characterized baryon number B, strangeness S and electric charge Q. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. All hadronic properties like masses, spectral functions etc. are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD). Decay chains of single Hagedorn states provide a well description of experimentally observed multiplicity ratios of strange and multi-strange particles. In addition, the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature TH. Box calculations including these Hagedorn states are performed. Indeed, the time scales leading to equilibration of the system are drastically reduced down to 2…5fm/c.

Is hadronic flow produced in p–Pb collisions at the Large Hadron Collider?

Using the Ultra-relativistic Quantum Molecular Dynamics ({\tt UrQMD}) model, we investigate the azimuthal correlations in p--Pb collisions at $\sqrt{s_{_{\rm NN}}}=5.02$ TeV. It is shown that the simulated hadronic p--Pb system can not generate the collective flow signatures, but mainly behaves as a non-flow dominant system. However, the characteristic $v_{2}(p_{\rm T})$ mass-ordering of pions, kaons and protons is observed in {\tt UrQMD} simulations, which is the consequence of hadronic interactions and not necessarily associated with strong fluid-like expansions.

Dilepton production and reaction dynamics in heavy-ion collisions at SIS energies from coarse-grained transport simulations

Dilepton invariant-mass spectra for heavy-ion collisions at SIS 18 and BEVALAC energies are calculated using a coarse-grained time evolution from the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model. The coarse-graining of the microscopic simulations enables to calculate thermal dilepton emission rates by application of in-medium spectral functions from equilibrium quantum-field theoretical calculations. The results show that extremely high baryon chemical potentials dominate the evolution of the created hot and dense fireball. Consequently, a significant modification of the $\rho$ spectral shape becomes visible in the dilepton invariant-mass spectrum, resulting in an enhancement in the low-mass region $M_{ee} = 200$ to 600 MeV/$c^{2}$. This enhancement, mainly caused by baryonic effects on the $\rho$ spectral shape, can fully describe the experimentally observed excess above the hadronic cocktail contributions in Ar+KCl ($E_{\mathrm{lab}}=1.76$ $A$GeV) reactions as measured by the HADES collaboration and also gives a good explanation of the older DLS Ca+Ca ($E_{\mathrm{lab}}=1.04$ $A$GeV) data. For the larger Au+Au ($E_{\mathrm{lab}}=1.23$ $A$GeV) system, we predict an even stronger excess from our calculations. A systematic comparison of the results for different system sizes from C+C to Au+Au shows that the thermal dilepton yield increases stronger ($\propto A^{4/3}$) than the hadronic background contributions, which scale with $A$, due to its sensitivity on the time evolution of the reaction. We stress that the findings of the present work are consistent with our previous coarse-graining results for the NA60 measurements at top SPS energy. We argue that it is possible to describe the dilepton results from SIS 18 up to SPS energies by considering the modifications of the $\rho$ spectral function inside a hot and dense medium within the same model.

Investigation of possible hadronic flow insNN=5.02TeVp−Pbcollisions

Using the ultrarelativistic quantum molecular dynamics (UrQMD) model, we investigate azimuthal correlations in $p\ensuremath{-}\mathrm{Pb}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=5.02\phantom{\rule{0.28em}{0ex}}\mathrm{TeV}$. Comparison with the experimental data shows that UrQMD cannot reproduce the multiplicity dependence of two- and four-particle cumulants, especially the transition from positive to negative values of ${c}_{2}{4}$ in high-multiplicity events, which has been taken as experimental evidence of collectivity in $p\ensuremath{-}\mathrm{Pb}$ collisions. Meanwhile, UrQMD cannot describe the differential elliptic flow ${v}_{2}({p}_{\mathrm{T}})$ of all charged hadrons at various multiplicity classes. These discrepancies show that the simulated hadronic $p\ensuremath{-}\mathrm{Pb}$ systems cannot generate enough collective flow as observed in experiment, the associated hadron emissions are largely influenced by nonflow effects. However, the characteristic ${v}_{2}({p}_{\mathrm{T}})$ mass ordering of pions, kaons, and protons is observed in UrQMD, which is the consequence of hadronic interactions and not necessarily associated with strong fluid-like expansions.

Coarse-graining approach for dilepton production at energies available at the CERN Super Proton Synchrotron

Coarse-grained output from transport calculations is used to determine thermal dilepton emission rates by applying medium-modified spectral functions from thermal quantum field theoretical models. By averaging over an ensemble of events generated with the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) transport model, we extract the local thermodynamic properties at each time step of the calculation. With an equation of state the temperature $T$ and chemical potential ${\ensuremath{\mu}}_{\mathrm{B}}$ can be determined. The approach goes beyond simplified fireball models of the bulk-medium evolution by treating the full (3+1)-dimensional expansion of the system with realistic time and density profiles. For the calculation of thermal dilepton rates we use the in-medium spectral function of the $\ensuremath{\rho}$ meson developed by Rapp and Wambach and consider thermal quark-gluon plasma (QGP) and multipion contributions as well. The approach is applied to the evaluation of dimuon production in In+In collisions at top CERN Super Proton Synchrotron (SPS) energy. Comparison to the experimental results of the NA60 experiment shows good agreement of this ansatz. We find that the experimentally observed low-mass dilepton excess in the mass region from 0.2 to 0.6 GeV can be explained by a broadening of the $\ensuremath{\rho}$ spectral function with a small mass shift. In contrast, the intermediate-mass region $(M>1.5$ GeV) is dominated by a contribution from the quark-gluon plasma. These findings agree with previous calculations with fireball parametrizations. This agreement, in spite of differences in the reaction dynamics between both approaches, indicates that the time-integrated dilepton spectra are not very sensitive to details of the space-time evolution of the collision.

Mass-splitting effect on flows in heavy-ion collisions in the Fermi-energy domain

In this work, based on one updated version of the ultrarelativistic quantum molecular dynamics (UrQMD) model in which the Skyrme-like (parabolic) isospin- and momentum-dependent interaction is included, the effect of the neutron-proton effective mass splitting (NPEMS) on flows in heavy-ion collisions at the Fermi-energy domain (between 40 and 100 MeV/nucleon) is focused. Using various Skyrme interactions (all exhibiting similar values of isoscalar incompressibility but very different NPEMS), both rapidity- and transverse-momentum-dependent directed and elliptic flows of free neutrons and protons are calculated. Our calculations show that the effect of NPEMS on the flows of free nucleons is more obvious at ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$ than at $40 \mathrm{MeV}/\mathrm{nucleon}$. At ${E}_{\mathrm{lab}}=100\phantom{\rule{0.16em}{0ex}}\mathrm{MeV}/\mathrm{nucleon}$, the directed flows of both neutrons and protons are easily affected by the NPEMS, while the elliptic flow of protons is not very sensitive to the NPEMS at both energies. It is suggested that the directed flow is better than the elliptic flow for probing the NPEMS.

Strongly intensive measures for particle number fluctuations: effects of hadronic resonances

The strongly intensive measures Δ and Σ are used to study event-by-event fluctuations of hadron multiplicities in nucleus–nucleus collisions. The effects of resonance decays are investigated using a statistical model and a relativistic transport model. Two specific examples are considered: resonance decays to two positively charged particles (e.g., ) and to pairs (e.g., ). It is shown that resonance abundances at the chemical freeze-out can be estimated by measuring the fluctuations of the number of stable hadrons. These model results are compared against a full hadronresonance gas analysis within both the grand canonical and canonical ensembles. The ultra-relativistic quantum molecular dynamics (UrQMD) model of nucleus–nucleus collisions is used to illustrate the role of global charge conservation, centrality selection, and limited experimental acceptance.

Systematic study of the elliptic flow parameter using a transport approach

Elliptic flow parameter, v2 is considered as a sensitive probe for early dynamics of the heavy-ion collision. In this work, we have discussed the effect of detector efficiency, procedure of centrality determination, effect of resonance decay and the procedure to correct event plane resolution on the measured v2 by standard event plane method within the framework of a transport model. The measured value of v2 depends on the efficiency in particle number counting by the detector. The effect of centrality determination is found to be negligible. The new method of event plane resolution correction for wide centrality bin yields results in v2 values closer to the true value of the v2. The contributions from the resonance decay seems to decrease the value of v2 of π and K within the Ultra relativistic Quantum Molecular Dynamics (UrQMD) model based calculation. We also propose a procedure to correct for an event bias effect on v2 arising while comparing the minimum bias collision centrality v2 values for different multi-strange hadrons. Finally, we have presented a model based confirmation of the recently proposed relation between v2 obtained using event plane method and scalar product method to the true value of v2.

3H/3He ratio as a probe of the nuclear symmetry energy at sub-saturation densities

Within the newly updated version of the Ultra-relativistic quantum molecular dynamics (UrQMD) model in which the Skyrme potential energy-density functional is introduced, the yield ratio between $^3$H and $^3$He clusters emitted from central $^{40}$Ca+$^{40}$Ca, $^{96}$Zr+$^{96}$Zr, $^{96}$Ru+$^{96}$Ru, and $^{197}$Au+$^{197}$Au collisions in the beam energy range from 0.12 to 1 GeV$/$nucleon is studied. The recent FOPI data for the $^3$H$/$$^3$He ratio are compared with UrQMD calculations using 13 Skyrme interactions (all exhibiting similar values of iso-scalar incompressibility but very different density dependences of the symmetry energy). It is found that the $^3$H$/$$^3$He ratio is sensitive to the nuclear symmetry energy at sub-saturation densities. Model calculations with moderately soft to linear symmetry energies are in agreement with the experimental FOPI data. This result is in line with both, the recent constraints on the low-density symmetry energy available in the literature and our previous results for the high-density symmetry energy obtained with the elliptic flow of free nucleons and hydrogen isotopes as a sensitive probe.

Ideal Fluids, the Quark Gluon Plasma, and Hadronic Gases

A detailed comparison between two methods to calculate the shear viscosity coefficient of a hot hadronic gas is presented. We choose two systems in this comparison which are massless particles with current algebra cross section and a mixture comprised of pions with rho resonances. The two methods involved are the Green-Kubo method, applied using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model to simulate the hadronic medium, and the Chapman-Enskog method. In addition, the effect of the resonance lifetime on the shear viscosity coefficient is investigated.

Mean transverse mass of hadrons in proton–proton reactions

An energy dependence of the mean transverse mass $\langle m_T\rangle$ at mid-rapidity in proton-proton ($p+p$) reactions is studied within the ultra-relativistic quantum molecular dynamics (UrQMD). The UrQMD model predicts a nonmonotonous dependence of $\langle m_T\rangle$ on collision energy for several hadron species: for $\pi^+$, $p$, $K^+$, and $\Lambda$ the mean transverse mass has a maximum at the center of mass energy region $5\le \sqrt{s}\le 8$ GeV. These results are a consequence of an interplay of two contributions: 1) excitations and decays of the baryonic resonances $N^*$ and $\Delta$; 2) excitations and decays of the baryonic strings. The UrQMD results do not show any nonmonotonous dependence of $\langle m_T\rangle$ on $\sqrt{s}$ for $\pi^-$, $K^{-}$, and antiprotons. Whether a nonmonotonous dependence of $\langle m_T\rangle$ at mid-rapidity on the collision energy for $\pi^+$, $p$, $K^+$, and $\Lambda$ is relevant for real $p+p$ interactions will be soon checked experimentally by the NA61/SHINE Collaboration.

Multifractal detrended fluctuation analysis of particle density fluctuations in high-energy nuclear collisions

The detrended fluctuation analysis (DFA) and the multifractal DFA (MF-DFA) techniques are employed to characterize the pseudorapidity (η) distribution of charged mesons produced in 28Si+Ag/Br interaction at 14.5 GeV/nucleon and 32S+Ag/Br interaction at 200 GeV/nucleon. Various multifractal parameters are calculated and compared with a Monte-Carlo simulation based on the ultra-relativistic quantum molecular dynamics (UrQMD) model. The results of this analysis show that the single particle distributions in both experiments and in their respective UrQMD simulations are multifractal in nature. The differences between the experiment and corresponding simulation however, are not always very significant. But the present results are significantly different from those obtained by using other conventional methods of multifractal analysis. The observations also indicate that the detrended multifractal analysis might be an efficient tool for characterizing the multiparticle emission data, but the method requires some improvement so that it can differentiate between the non-statistical signal and the statistical noise.

Remarkable Features of Decaying Hagedorn States

Hagedorn states (HS) are a tool to model the hadronization process which occurs in the phase transition phase between the quark gluon plasma (QGP) and the hadron resonance gas (HRG). Their abundance is believed to appear near the Hagedorn temperature TH which in our understanding equals the critical temperature Tc. These hadron-like resonances are characterized by being very massive and by not being limited to quantum numbers of known hadrons. To generate a whole zoo of such new states we solve the covariantly formulated bootstrap equation by regarding energy conservation and conservation of the baryon number B, strangeness S and electric charge Q. To investigate their decay properties decay chain calculations of HS were conducted. One single (heavy) HS with certain quantum numbers decays by various two-body decay channels subsequently into final stable hadrons. Multiplicities of these stable hadrons, their ratios and their energy distributions are presented. Strikingly the final energy spectra of resulting hadrons show a thermal-like distribution with the characteristic Hagedorn temperature TH. All hadronic properties like masses, spectral functions etc. are taken from the hadronic transport model Ultra Relativistic Quantum Molecular Dynamics (UrQMD).

Hadronic Shear Viscosity: A Comparison between the Green-Kubo and Chapmann Enskog Methods

A detailed comparison between two methods to calculate shear viscosity is presented. We choose two systems in this comparison which are massless particles with current algebra cross section and a mixture comprised of pions with rho resonances. The two methods involved are the Green-Kubo method, applied using the Ultrarelativistic Quantum Molecular Dynamics (UrQMD) model to simulate the hadronic medium, and the Chapmann-Enskog method.

Effect of the spin-orbit interaction on flows in heavy-ion collisions at intermediate energies

The effect of the spin-orbit coupling in heavy ion collisions is investigated based on an updated version of the ultra-relativistic quantum molecular dynamics (UrQMD) model, in which the Skyrme potential energy density functional is employed. And in special, the spin-orbit coupling effects on the directed and elliptic flows of free nucleons emitted from $^{197}$Au+$^{197}$Au collisions as functions of both the beam energy and the impact parameter are studied. Our results show that the net contribution of the spin-orbit term to flows of nucleons is negligible, whereas a directed flow splitting between spin-up and spin-down nucleons is visible especially at large impact parameters and a peak of the splitting is found at the beam energy around 150 MeV$/$nucleon. We also found that the directed flow splitting between spin-up and spin-down neutrons is comparable with the neutron directed flow difference calculated by a soft and a stiff symmetry energy, indicating that the directed flow of neutrons cannot be used to pin down the stiffness of symmetry energy any more without considering the spin degree of freedom in models in case of spin polarization.

The effect of inner magnetic field on collective flows from heavy-ion collisions at intermediate energies

The properties of nuclear matter under extreme conditions (high temperature, density and isospin-asymmetry) have attracted a lot of attention in recent years. At present, heavy ion reactions in combination with corresponding model simulations are among the most important ways to investigate this subject. It is known that a strong inner magnetic field is created during the heavy ion collisions. Nevertheless, its effects on the motion of charged particles are usually not taken into account in previous transport model simulations for simplicity. Within the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) model, the effect of inner magnetic field on the emission of several charged particles is investigated. It is found that its effect on emitted nucleon related observables, such as yields and collective flows, is weak, while it is visible on pion related observables, such as π--π+ yield ratio and flows, as a function of rapidity. This result implies that it is necessary to consider the effect of inner magnetic field especially when the π mesons emitted from heavy ion collisions at intermediate energies are taken as a sensitive probe for the properties of nuclear matter.

Azimuthal structure of charged particle emission in 28Si–Ag/Br interaction at 14.5A GeV and 32S–Ag/Br interaction at 200A GeV

Presence of unusual azimuthal structures in the particle emission data obtained from the 28 Si – Ag / Br interaction at 14.5A GeV and from the 32 S – Ag / Br interaction at 200A GeV, are investigated in the framework of the Cherenkov gluon emission and/or Mach shock wave formation in nuclear/partonic medium. Nuclear photographic emulsion technique is used to collect the experimental data. The experiment is compared with the predictions of two simulations, namely (i) the Relativistic Quantum Molecular Dynamics (RQMD) and (ii) the Ultra-relativistic Quantum Molecular Dynamics (UrQMD). A charge reassignment algorithm is implemented over the outputs of the simulations to mimic the Bose–Einstein correlation (BEC) effect. Our analysis confirms presence of jet-like structures in both experiments beyond statistical noise. Such structures are more pronounced in the 32 S data than in the 28 Si data.