Elliptic Flow Of Protons Research Articles

QCD Equation of State of Dense Nuclear Matter from a Bayesian Analysis of Heavy-Ion Collision Data.

Bayesian methods are used to constrain the density dependence of the QCD equation of state (EOS) for dense nuclear matter using the data of mean transverse kinetic energy and elliptic flow of protons from heavy ion collisions (HICs), in the beam energy range sqrt[s_{NN}]=2-10 GeV. The analysis yields tight constraints on the density dependent EOS up to 4 times the nuclear saturation density. The extracted EOS yields good agreement with other observables measured in HIC experiments and constraints from astrophysical observations both of which were not used in the inference. The sensitivity of inference to the choice of observables is also discussed.

Flow and interferometry results from Au+Au collisions at sNN=4.5 GeV

The beam energy scan (BES) program at the BNL Relativistic Heavy Ion Collider (RHIC) was extended to energies below sNN=7.7 GeV in 2015 by successful implementation of the fixed-target mode of operation in the STAR (Solenoidal Tracker At RHIC) experiment. In this mode, ions circulate in one ring of the collider and interact with a stationary target at the entrance of the STAR time projection chamber. The first results for Au+Au collisions at sNN=4.5 GeV are presented, demonstrating good performance of all the relevant detector subsystems in fixed-target mode. Results presented here include directed and elliptic flow of identified hadrons, and radii from pion femtoscopy. The latter, together with recent HADES results, reveal a long-sought peak structure that may be caused by the system evolving through a first-order phase transition from quark-gluon plasma to the hadronic phase. Directed and elliptic flow for pions are presented for the first time at this beam energy. Pion and proton elliptic flow show behavior which hints at constituent quark scaling, and demonstrate that a definitive conclusion will be achievable using the full statistics of the ongoing second phase of BES (BES-II). In particular, BES-II to date has recorded fixed-target data sets with two orders of magnitude more events at each of nine energies between sNN=3.0 and 7.7 GeV.13 MoreReceived 29 July 2020Revised 12 December 2020Accepted 2 March 2021DOI:https://doi.org/10.1103/PhysRevC.103.034908©2021 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasCollective flowParticle correlations & fluctuationsRelativistic heavy-ion collisionsNuclear Physics

Momentum-dependent potential and collective flows within the relativistic quantum molecular dynamics approach based on relativistic mean-field theory

Relativistic quantum molecular dynamics based on the relativistic mean field theory (RQMD.RMF) is extended by including momentum-dependent potential. The equation of state (EoS) dependence of the directed and the elliptic flow of protons in the beam energy range of $2.3 < \sqrt{s_{NN}}< 20$ GeV is examined. It is found that the directed flow depends strongly on the optical potential at high energies,$\sqrt{s_{NN}} > 3 $ GeV, where no information is available experimentally. The correlation between effective mass at saturation density and the optical potential is found: smaller values of effective mass require smaller strengths of the optical potential to describe the directed flow data.This correlation can also be seen in the beam energy dependence of the elliptic flow at $\sqrt{s_{NN}}>3$ GeV, although its effect is rather weak. On the other hand, stiff EoS is required to describe the elliptic flow at lower energies.Experimental constraints on the optical potential from $pA$ collisions will provide important information on the EoS at high energies.The proton directed and the elliptic flow are well described in the RQMD.RMF model from $\sqrt{s_{NN}}=2.3$ to 8.8 GeV. In contrast,to reproduce the collapse of the directed flow above 10 GeV, pressure has to be reduced, which indicates a softening of the EoS around $\sqrt{s_{NN}} =10 $ GeV.

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.

Isospin-sensitive observables as a probe of proton transition momentum in the HMT * * Partially supported by the National Natural Science Foundation of China (11875152, 11675066, U1867207, 11505085)

Based on the IBUU transport model, the effect of proton transition momentum on collective flows is studied in 40Ca + 40Ca,112Sn + 112Sn, and 197Au + 197Au collisions at an incident beam energy of 400 MeV/A with impact parameter . It is found that in a neutron rich system, the difference between neutron and proton elliptic flow is largely affected by the proton transition momentum. At beam energies around (and particularly below) the pion production threshold, the ratio is greatly sensitive to proton transition momentum in asymmetric nuclear matter. This study may help us to understand the nucleon momentum distribution in nuclei, which is important for the equation of state of asymmetric nuclear matter, such as neutron stars.

Recent results for STAR [formula omitted] Al+Au and [formula omitted] Au+Au Fixed-Target Collisions

We present recent results from Al(beam)+Au(target) collisions at sNN=4.9GeV and Au+Au collisions at sNN=4.5GeV from the STAR fixed-target (FXT) program. We report transverse mass spectra of protons, KS0 and Λ, rapidity density distributions of π±, KS0 and Λ, directed flow of protons, π±, KS0 and Λ, and elliptic flow of protons and π±. These are the first measurements of pion directed and elliptic flow in this energy region. Pion and proton elliptic flow show mass ordering. Measurements are compared with published results from AGS and RHIC. These results demonstrate that the STAR detector performs well in the FXT configuration.

Effects of density- and momentum-dependent potentials in Au+Au collisions at intermediate energies**Supported by National Natural Science Foundation of China (11505150), China Postdoctoral Science Foundation (2015M582730) and Yuncheng University Research Project (YQ-2014014)

Based on an isospin-dependent transport model, the effects of the density- and momentum-dependent potentials are studied by simulating Au on Au collisions at 90, 120, 150 and 400 MeV/nucleon. It is found that the calculated results overestimate the experimental data on the directed flow and underestimate the data on the elliptic flow for protons. The impact of the density- and momentum-dependent potentials is observed in the mid-rapidity region of the final spectra. At 90 MeV/nucleon, the momentum-dependent potential has a larger impact on the observables than the density-dependent potential, and the elliptic flow has a higher value with the positive effective mass splitting. At 400 MeV/nucleon, however, the opposite is observed. The rapidity dependence of the elliptic flow for protons is sensitive to the symmetry energy. A soft symmetry energy corresponds to a higher value of the proton elliptic flow.

Self-consistent conversion of a viscous fluid to particles

Comparison of hydrodynamic and "hybrid" hydrodynamics+transport calculations to heavy-ion data inevitably requires the conversion of the fluid to particles. For dissipative fluids the conversion is ambiguous without additional theory input complementing hydrodynamics. We obtain self-consistent shear viscous phase space corrections from linearized Boltzmann transport theory for a gas of hadrons. These corrections depend on the particle species, and incorporating them in Cooper-Frye freezeout affects identified particle observables. For example, with additive quark model cross sections,proton elliptic flow is larger than pion elliptic flow at moderately high $p_T$ in $Au+Au$ collisions at RHIC. This is in contrast to Cooper-Frye freezeout with the commonly used "democratic Grad" ansatz that assumes no species dependence. Various analytic and numerical results are also presented for massless and massive two-component mixtures to aid the interpretation. Self-consistent viscous corrections for each species are tabulated in Appendix F for convenient inclusion in pure hydrodynamic and hybrid calculations.

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.

Elliptic flow of protons and antiprotons in Au + Au collisions at [formula omitted] within alternative scenarios of three-fluid dynamics

Analysis of elliptic flow of protons and antiprotons in Au + Au collisions is performed in a wide range of incident energies sNN=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 certainly preferable for the antiproton elliptic flow. The fact that difference between elliptic flows of protons and antiprotons decreases with the incident energy rise is a consequence of reducing baryon stopping rather than an onset of deconfinement.

Disentangling effects of collision geometry and symmetry energy in U+U collisions

Effects of the collision geometry on experimental observables that are known to be sensitive to the high-density behavior of nuclear symmetry energy are examined in U $+$ U collisions at 0.52 GeV/nucleon using an isospin- and momentum-dependent interaction within the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model. It is found that the neutron-proton differential flow in tip-tip collisions and the difference of neutron and proton elliptic flow in body-body collisions are more sensitive to the symmetry energy at suprasaturation densities compared with collisions of spherical nuclei of the same masses. In addition, the $n/p$ ratio of preequilibrium nucleons is found to be slightly more sensitive to the symmetry energy in tip-tip collisions, and the collision geometry affects the ${\ensuremath{\pi}}^{\ensuremath{-}}/{\ensuremath{\pi}}^{+}$ ratio significantly.

Elliptic flow of charged pions, protons and strange particles emitted in Pb+Au collisions at top SPS energy

Differential elliptic flow spectra v 2 ( p T ) of π − , K S 0 , p , Λ have been measured at s NN = 17.3 GeV around midrapidity by the CERN-CERES/NA45 experiment in mid-central Pb + Au collisions (10% of σ geo ). The p T range extends from about 0.1 GeV/ c (0.55 GeV/ c for Λ ) to more than 2 GeV/ c . Protons below 0.4 GeV/ c are directly identified by d E / d x . At higher p T , proton elliptic flow is derived as a constituent, besides π + and K + , of the elliptic flow of positive pion candidates. This retrieval requires additional inputs: (i) of the particle composition, and (ii) of v 2 ( p T ) of positive pions. For (i), particle ratios obtained by NA49 are adapted to CERES conditions; for (ii), the measured v 2 ( p T ) of negative pions is substituted, assuming π + and π − elliptic flow magnitudes to be sufficiently close. The v 2 ( p T ) spectra are compared to ideal-hydrodynamics calculations. In synopsis of the series π − – K S 0 – p – Λ , flow magnitudes are seen to fall with decreasing p T progressively even below hydro calculations with early kinetic freeze-out ( T f = 160 MeV ) leaving not much time for hadronic evolution. The proton v 2 ( p T ) data show a downward swing towards low p T with excursions into negative v 2 values. The pion-flow isospin asymmetry observed recently by STAR at RHIC, invalidating in principle our working assumption, is found in its impact on proton flow bracketed from above by the direct proton flow data, and not to alter any of our conclusions. Results are discussed in perspective of recent viscous hydrodynamics studies which focus on late hadronic stages.

Neutron–proton elliptic flow difference as a probe for the high density dependence of the symmetry energy

We employ an isospin dependent version of the QMD transport model to study the influence of the isospin dependent part of the nuclear matter equation of state and in-medium nucleon–nucleon cross-sections on the dynamics of heavy-ion collisions at intermediate energies. We find that the extraction of useful information on the isospin-dependent part of the equation of state of nuclear matter from proton or neutron elliptic flows is obstructed by their sensitivity to model parameters and in-medium values of nucleon–nucleon cross-sections. Opposite to that, neutron–proton elliptic flow difference shows little dependence on those variables while its dependence on the isospin asymmetric EoS is enhanced, making it more suitable for a model independent constraining of the high-density behaviour of asy-EoS. Comparison with existing experimental FOPI-LAND neutron–hydrogen data can be used to set an upper limit to the softness of asy-EoS. Successful constraining of the asy-EoS via neutron–proton elliptic flow difference will require experimental data of higher accuracy than presently available.

Relativistic heavy-ion collisions within three-fluid hydrodynamics: Hadronic scenario

A three-fluid hydrodynamic model for simulating relativistic heavy-ion collisions is introduced. Along with two baryon-rich fluids, the new model considers the time-delayed evolution of a third, baryon-free (i.e., with zero net baryonic charge) fluid of newly produced particles. Its evolution is delayed because of a formation time \ensuremath{\tau}, during which the baryon-free fluid neither thermalizes nor interacts with the baryon-rich fluids. After the formation it starts to interact with the baryon-rich fluids and quickly gets thermalized. Within this model with pure hadronic equation of state, a systematic analysis of various observables at incident energies between few and about 160A GeV has been done as well as a comparison with results of transport models. We have succeeded in reasonably reproducing a great body of experimental data in the incident energy range of ${E}_{\mathrm{lab}}\ensuremath{\simeq}$ (1--160)A GeV. The list includes proton and pion rapidity distributions, proton transverse-mass spectra, rapidity distributions of \ensuremath{\Lambda} and $\overline{\ensuremath{\Lambda}}$ hyperons, elliptic flow of protons and pions (with the exception of proton ${v}_{2}$ at 40A GeV), multiplicities of pions, positive kaons, \ensuremath{\phi} mesons, hyperons, and antihyperons, including multistrange particles. This agreement is achieved on the expense of substantial enhancement of the interflow friction as compared to that estimated proceeding from hadronic free cross sections. However, we have also found out certain problems. The calculated yield of ${K}^{\ensuremath{-}}$ is approximately higher than that in the experiment by a factor of 1.5. We have also failed to describe directed transverse flow of protons and pion at ${E}_{\mathrm{lab}}\ensuremath{\ge}40A$ GeV. This failure apparently indicates that the used EOS is too hard and thereby leaves room for a phase transition.

Anisotropic flow in4.2AGeV/cC+Tacollisions

Anisotropic flow of protons and negative pions in $4.2A\mathrm{GeV}/c$ $\mathrm{C}+\mathrm{Ta}$ collisions is studied using the Fourier analysis of azimuthal distributions. The protons exhibit pronounced directed flow. Directed flow of pions is positive in the entire rapidity interval and indicates that the pions are preferentially emitted in the reaction plane from the target to the projectile. The elliptic flow of protons and negative pions is close to zero. Comparison with the quark-gluon-string model and relativistic transport model show that they both yield a flow signature similar to the experimental data.

Centrality and momentum-selected elliptic flow: Tighter constraints for the nuclear equation of state

Proton elliptic flow is studied as a function of impact-parameter $b$, for two transverse momentum cuts in 2 - 6 AGeV Au + Au collisions. The elliptic flow shows an essentially linear dependence on b (for $1.5 < b < 8$ fm) with a negative slope at 2 AGeV, a positive slope at 6 AGeV and a near zero slope at 4 AGeV. These dependencies serve as an important constraint for discriminating between various equations of state (EOS) for high density nuclear matter, and they provide important insights on the interplay between collision geometry and the expansion dynamics. Extensive comparisons of the measured and calculated differential flows provide further evidence for a softening of the EOS between 2 and 6 GeV/nucleon.

Eventanisotropy in 4.2A GeV c-1 C + C collisions

The directed and elliptic flow of protons and negative pions in4.2A GeV c-1C + C collisions is studied using the Fourier analysis of azimuthaldistributions. It is found that the protons exhibit pronounced directedflow, while the flow of pions is either non-existent or too weak to bedetected experimentally. Also, it is found that in the entire rapidityinterval the elliptic flow is very small if not zero. These results areconfirmed by the quark-gluon-string model (QGSM)and the relativistic transport model (ART 1.0), except that these modelspredict a very weak antiflow of pions. The more detailed comparison withthe QGSM suggests that the decay of resonances and rescattering ofsecondaries dominantly determine the proton and negative pion flow atthis energy.

Directed and elliptic flow in 158 AGeV Pb+Pb collisions

Directed and elliptic flow of protons and positively charged pions has been studied in the target fragmentation region using the Plastic Ball detector in the WA98 experiment. The results exhibit a strong dependence on centrality, rapidity, and transverse momentum. The rapidity dependence can be described by a Gaussian distribution. The model comparisons reveal a large discrepancy of the flow strength obtained from the data and the simulations.

Elliptic Flow in Heavy-Ion Collisions near the Balance Energy

The proton elliptic flow in collisions of Ca on Ca at energies from 30 to 100 MeV/nucleon is studied in an isospin-dependent transport model. With increasing incident energy, the elliptic flow shows a transition from positive to negative flow. Its magnitude depends on both the nuclear equation of state (EOS) and the nucleon-nucleon scattering cross section. Different elliptic flows are obtained for a stiff EOS with free nucleon-nucleon cross sections and a soft EOS with reduced nucleon-nucleon cross sections, although both lead to vanishing in-plane transverse flow at the same balance energy. The study of both in-plane and elliptic flows at intermediate energies thus provides a means to extract simultaneously the information on the nuclear equation of state and the nucleon-nucleon scattering cross section in medium.

Elliptic Flow: Transition from Out-of-Plane to In-Plane Emission inAu+AuCollisions

We have measured the proton elliptic flow excitation function for the Au + Au system spanning the beam energy range 2 -- 8 AGeV. The excitation function shows a transition from negative to positive elliptic flow at a beam energy, $E_{tr} \sim$ 4 AGeV. Detailed comparisons with calculations from a relativistic Boltzmann-equation are presented. The comparisons suggest a softening of the nuclear equation of state (EOS) from a stiff form (K \sim 380 MeV) at low beam energies (E_{Beam} \le 2 AGeV) to a softer form (K \sim 210 MeV) at higher energies (E_{Beam} \ge $ 4 AGeV) where the calculated baryon density $ \rho \sim 4 \rho_0$.