Number-of-constituent-quark scaling of elliptic flow:a quantitative study

The number-of-constituent-quark(NCQ)scaling behavior of the elliptic flow of identified particles produced in A+A collisions is studied quantitatively using an empirical function that fits the experimental v_(2) data available from the RHIC and LHC.The most common approach for NCQ scaling involves(1)doing a scaling of the experimental v_(2) data of an identified particle with its NCQ,(2)doing the same to its transverse momentum or energy,then(3)combining all the scaled data and identifying the NCQ behavior by intuitively looking(since the measured experimental data are discrete).We define two variables(d_(1),d_(2))to describe NCQ scaling quantitatively and simultaneously,and identify the approximate region where the NCQ scaling holds.This approach could be applied to study NCQ or other scaling phenomena in future experiments.

The Evolution of Elliptic Flow Under First Order Phase Transition

Elliptic flow for non-central Au＋Au collisions at √SNN=200 GeV is investigated with a 2＋1 dimensional hydrodynamic model. We analyze the softening effect by the velocity along the axis. The contribution of the elliptic flow from the QGP phase, mixed phase and hadron gas phase is studied. The relation between the sound horizon and evolution of the elliptic flow is discussed.

The Elliptic Flow of Multi-Strange Hadrons in [S_(NN)]^(1/2)= 200 GeV Au + Au Collisions at STAR

Azimuthal anisotropy, especially for the multi-strange hadrons, is expected to be sensitive to the dynamical evolution in the early stage of high energy nuclear collisions. In this paper we present the latest results of multi-strange hadron elliptic flow in Au ＋ Au collisions at √SNN=200GeV from the STAR experiment at RHIC. The number-of-quark scaling is evidenced with φ（ss） and Ω（sss） with highly statistical data, which shows strange quark collectivity at RHIC. The u2 of φ meson is found to be consistent with that of proton within statistical error bars at pw 〈 1 GeV/c.

Elliptic Flow Splitting between Particles and their Antiparticles in Au＋Au Collisions from a Multiphase Transport Model

The elliptic flow v2, for π±, K±, p and p in Au＋Au collisions at center-of-mass energies √sNN=7.7, 11.5, 14.5 and 19.6 GeV, is analyzed using a multiphase transport model. A significant difference in the v2 values for p and p is observed, and the values of v2 splitting are larger compared with π＋ and π-, K＋ and K-. The difference increases with decreasing the center-of-mass energy. The effect of the quark coalescence mechanism in a multi-phase transport model to the value of elliptic difference △v2 between p and p- has been discussed. The simulation of Au＋Au collisions at 14.5 GeV shows that the effect of hadron cascade to △v2 is not obvious, and a larger patton-scattering cross section can lead to a larger △v2.

An explanation for deviations from the quark number scaling of elliptic flows in low P_T region

We carry out a systematic study of the different contributions to the deviations of the elliptic flows from the quark number scaling in high energy heavy ion collision in a quark combination model. The effects that we considered are： the resonance decay, the flavor dependence of the quark elliptic flow and the combination of quarks/antiquarks with slightly different transverse momenta. Our results show that the deviations observed in experiments can be well reproduced within the combination framework if all the three effects are considered. We make a detailed analysis of the different contributions using a Monte-Carlo program and suggest measuring the quark number scaling in intermediate PT range more precisely.

Eccentricity fluctuations are not the only source of elliptic flow fluctuations in a multiphase transport model

Sources of event-by-event elliptic flow fluctuations in relativistic heavy-ion collisions are investigated in a multiphase parton transport model （AMPT）. Besides the well-known initial eccentricity fluctuations, several other sources of elliptic flow dynamical fluctuations are identified. One is fluctuations in initial parton configurations at a given eccentricity. Configuration fluctuations are found to be as important as eccentricity fluctuations in elliptic flow development. A second is quantum fluctuations in parton-parton interactions during system evolution. A third is fluctuations caused by hadronization and final-state hadronic scatterings. The magnitudes of these fluctuations are investigated relative to the eccentricity fluctuations and the average elliptic flow magnitude. The fluctuations from the latter two sources are found to be negative. The results may have important implications for the interpretation of elliptic flow data.

Pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss interferometry in a viscous granular source model

We examine the evolution of quark-gluon plasma（QGP） droplets with viscous hydrodynamics and analyze the pion transverse-momentum spectrum, elliptic flow, and Hanbury-Brown-Twiss（HBT） interferometry in a granular source model consisting of viscous QGP droplets. The shear viscosity of the QGP droplet speeds up and slows down the droplet evolution in the central and peripheral regions of the droplet, respectively. The effect of the bulk viscosity on the evolution is negligible. Although there are viscous effects on the droplet evolution, the pion momentum spectrum and elliptic flow change little for granular sources with and without viscosity. On the other hand,the influence of viscosity on HBT radius Rout is considerable. It makes Rout decrease in the granular source model.We determine the model parameters of granular sources using the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii together, and investigate the effects of viscosity on the model parameters. The results indicate that the granular source model may reproduce the experimental data of pion transverse-momentum spectrum, elliptic flow, and HBT radii in heavy-ion collisions of Au-Au at√s（NN）=200 GeV and Pb-Pb at√s（NN） =2.76 Te V in different centrality intervals. The viscosity of the droplet leads to an increase in the initial droplet radius and a decrease of the source shell parameter in the granular source model.

Effects of elliptic flow and resonance decay process on the Kurtosis of net baryon distributions

Kurtosis is regarded as a meaningful and promising observable in searching for the possible critical point predicted by QCD. In this paper, the effects of elliptic flow and resonance decay process on the Kurtosis have been studied with Monte Carlo event generators in Au ＋ Au collisions at sNN^（1/2） = 200 GeV. The results show that the Kurtosis is not sensitive to elliptic flow and resonance decay process.

π-J/ψ correlation and elliptic flow parameter v_2 of charmed mesons at RHIC energy

We study the correlation between the trigger π and the associated J/ψ on near and away sides in Au＋Au collisions at sNN^（1/2） = 200 GeV. In the region of trigger momentum pt 〉 4 GeV/c, the π spectrum is composed of thermal-shower and shower-shower recombinations in the frame work of the recombination model. We consider the azimuthal anisotropy in the quenched hard parton distribution and then calculate the elliptic flow parameter v2 of charmed mesons （J/ψ, D0 and Ds） for different centralities.

An explanation of the elliptic flow difference between proton and anti-proton from the UrQMD model with hadron potentials

The time evolution of both proton and anti-proton v2 flows from Au＋Au collisions at √SNN=7.7 GeV are examined by using both pure cascade and mean-field potential versions of the UrQMD model. Due to a stronger repulsion at the early stage introduced by the repulsive potentials and hence much less annihilation probabilities, anti-protons are frozen out earlier with smaller v2 values. Therefore, the experimental data of anti-proton v2 as well as the flow difference between proton and anti-proton can be reasonably described with the potential version of UrQMD.

Eccentricity and elliptic flow at a fixed centrality in Au+Au collisions at (sNN)^(1/2)=200 GeV in an AMPT model

In this paper, elliptic flow is studied at fixed centrality in Au＋Au collision at √sNN=200 GeV in the AMPT model. It is observed that with the participant increasing, elliptic flow has an increase or a decrease at different fixed impact parameter, but it does not have a trivial fluctuation. It is analyzed that the initial space anisotropy dominates the participant dependence of elliptic flow in near-central collisions（b=5 fm） and mid-central collisions（b=8 fm）, while the interaction between particles can mainly answer for the behavior of elliptic flow with participant in peripheral collisions （b=12 fm）. To distinguish the pure geometrical effect, elliptic flow scaled by initial eccentricity is studied. It is found that the ratio v2/ε increases with participant and reaches a saturation when the participant is large enough, indicating that the collision system may reach the local equilibrium.

Effects of mean-field and softening of equation of state on elliptic flow in Au+Au collisions at (~SNN)^(1/2)=5 GeV from the JAM model

We perform a systematic study of elliptic flow（v2） in Au＋Au collisions at √^SNN = 5 GeV by using a microscopic transport model, JAM. The centrality, pseudorapidity, transverse momentum and beam energy dependence of v2 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 the 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 the EoS leads to the enhancement of v2, while the hadronic mean-field suppresses v2 relative to the cascade mode. It indicates that elliptic flow at high baryon density regions is highly sensitive to the EoS and the enhancement of v2 may probe the signature of a first-order phase transition in heavy-ion collisions at beam energies of a strong baryon stopping region.

Elliptic flow of direct photons in Au+Au collisions at 200 GeV

The rapidity dependence of the elliptic flow of direct photons in Au＋Au collisions at√ s NN = 200 GeV are predicted,based on a three-dimensional ideal hydrodynamic description of the hot and dense matter.The rapidity dependence of the elliptic flow v 2 （y） of direct photons （mainly thermal photons） is very sensitive to the initial energy density distribution along longitudinal direction,which provides a useful tool to extract the realistic initial condition from measurements.

Transverse radius dependence for transverse velocity and elliptic flow in intermediate energy HIC

The mean transverse velocity and elliptic flow of light fragments （A≤2） as a function of transverse radius are studied for 25 MeV/nucleon 64Cu＋64Cu collisions with impact parameters 3–5 fm by the isospin- dependent quantum molecular dynamics model. By comparison between the in-plane and the out-of-plane transverse velocities, the elliptic flow dependence on the transverse radius can be understood qualitatively, and variation of the direction of the resultant force on the fragments can be investigated qualitatively.

Energy dependence for directed and elliptic flow in intermediate-energy heavy ion collisions

Differential and integrated directed flow and elliptic flow of light charged particles （z ≤ 2） are studied systematically for semi-central （b = 5 fm） 197Au＋197Au collisions at incident energies from 25 to 250 MeV/nucleon by the isospin-dependent quantum molecular dynamics model. The changes of directed and elliptic flow with incident energy reflect the dynamic competition between mean field and nucleon-nucleon collisions and also between collective rotation and expansion.

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

By incorporating an iso spin-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 m*n-p=m*n-m*p/m and the density-dependent nuclear symmetry energy Esym(ρ)on the elliptic flow v2 in197Au+197 Au 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 Esym(ρ),and the variation of m*n-p ranging from-0.03 to 0.03 at saturation density with isospin asymmetryδ=(ρn-ρp)/ρ-0.2,the Esym(ρ)has a stronger influence on the difference in v2 between neutrons and protons,i.e.,v2n-v2p,than m*n-p has.Meanwhile,at lower beam energies(≤0.25 GeV/nucleon),v2n-v2p is sensitive to both the Esym(ρ)and the m*n-p.Moreover,the influence of m*n-p on v2n-v2p is more evident with the parameters of this study when using the soft,rather than stiff,symmetry energy.

The medium-temperature dependence of jet transport coefficient in high-energy nucleus-nucleus collisions

The medium-temperature T dependence of the jet transport coefficient̂q was studied via the nuclear modification factor RAA(p_(T))and elliptical flow parameter v_(2)(p_(T))for large transverse momentum p_(T) hadrons in high-energy nucleus-nucleus collisions.Within a next-to-leading-order perturbative QCD parton model for hard scatterings with modified fragmentation functions due to jet quenching controlled by q,we check the suppression and azimuthal anisotropy for large p_(T) hadrons,and extract q by global fits to RAA(pT)and v_(2)(pT)data in A+A collisions at RHIC and LHC,respectively.The numerical results from the best fits show that q∕T^(3) goes down with local medium-temperature T in the parton jet trajectory.Compared with the case of a constant q∕T^(3),the going-down T dependence of q∕T^(3) makes a hard parton jet to lose more energy near T_(c) and therefore strengthens the azimuthal anisotropy for large pT hadrons.As a result,v_(2)(p_(T))for large pT hadrons was enhanced by approximately 10%to better fit the data at RHIC/LHC.Considering the first-order phase transition from QGP to the hadron phase and the additional energy loss in the hadron phase,v_(2)(p_(T))is again enhanced by 5-10%at RHIC/LHC.

The Weak Magnetic Photon Emission from Quark-gluon Plasma

There must be electromagnetic fields created during high-energy heavy-ion collisions.Although the electromagnetic field may become weak with the evolution of the quark-gluon plasma(QGP),compared to the energy scales of the strong interaction,they are potentially important to some electromagnetic probes.In this work,we propose the coupled effect of the weak magnetic field and the longitudinal dynamics of the background medium for the first time.We demonstrate that the induced photon spectrum can be highly azimuthally anisotropic when the quarkgluon plasma is in the presence of a weak external magnetic field.On the other hand,the weak magnetic photon emission from quark-gluon plasma only leads to a small correction to the photon production rate.After hydrodynamic evolution with a tilted fireball configuration,the experimentally measured direct photon elliptic flow is well reproduced.Meanwhile,the used time-averaged magnetic field in the hydrodynamic stage is found no larger than a few percent of the pion mass square.

Anisotropic flow at RHIC

STAR’s measurement of directed flow for pions,kaons（K 0 S ）,protons and anti-protons,for Au＋Au collisions at 200 GeV obtained in Run7 are presented,as well as elliptic flow for identified particles measured in Au＋Au（Run7） and Cu＋Cu（Run5） collisions.It is found that the slope of proton v 1 （y） at midrapidity is extremely small.Elliptic flow results are compared to Hydro calculation and the discrepancy is discussed.

Subsonic Euler flows in a divergent nozzle

We characterize a class of physical boundary conditions that guarantee the existence and uniqueness of the subsonic Euler flow in a general finitely long nozzle.More precisely,by prescribing the incoming flow angle and the Bernoulli’s function at the inlet and the end pressure at the exit of the nozzle,we establish an existence and uniqueness theorem for subsonic Euler flows in a 2-D nozzle,which is also required to be adjacent to some special background solutions.Such a result can also be extended to the 3-D asymmetric case.