Elliptic Flow Parameter Research Articles

Elliptic flow inU+Ucollisions atsNN=200GeV and inPb+Pbcollisions atsNN=2.76TeV: Prediction from a hybrid approach

We predict the elliptic flow parameter v_2 in U+U collisions at sqrt{s_{NN}}=200 GeV and in Pb+Pb collisions at sqrt{s_{NN}} = 2.76 TeV using a hybrid model in which the evolution of the quark gluon plasma is described by ideal hydrodynamics with a state-of-the-art lattice QCD equation of state, and the subsequent hadronic stage by a hadron cascade model.

First measurement of J/ψ anisotropy by PHENIX experiment at RHIC

Understanding the J/ψ suppression and possible recombination mechanisms at RHIC is one of the outstanding challenges for theorists and experimentalists. Recent results provided by PHENIX showed a stronger suppression at forward rapidity, while at mid-rapidity the suppression is similar to lower energy collision experiments. A large sample of Au + Au collisions at \( \sqrt {s_{NN} } \) = 200 GeV was collected in 2007 with the PHENIX experiment at RHIC. Using this sample, J/ψs were identified in the di-electron decay channel. In order to probe the charm coalescence as an additional J/ψ production mechanism at RHIC, we studied the first determination of its v2 elliptic flow parameter at mid-rapidity.

Energy dependence of elliptic flow from heavy-ion collision models

We have compared the experimental data on charged particle elliptic flow parameter (v2) in Au+Au collisions at midrapidity for \surd sNN = 9.2, 19.6, 62.4 and 200 GeV with results from various models in heavy-ion collisions like UrQMD, AMPT, and HIJING. We observe that the average <v2> from the transport model UrQMD agrees well with the measurements at \surd sNN = 9.2 GeV but increasingly falls short of the experimental <v2> values as the beam energy increases. The difference in <v2> being of the order of 60% at \surd sNN = 200 GeV. The <v2> results from HIJING is consistent with zero, while those from AMPT with default settings, a model based on HIJING with additional initial and final state rescattering effects included, gives a <v2> value of about 4% for all the beam energies studied. This is in contrast to increase in <v2> with beam energy for the experimental data. A different version of the AMPT model, which includes partonic effects and quark coalescence as a mechanism of hadronization, gives higher values of <v2> among the models studied and is in agreement with the measured <v2> values at \surd sNN = 200 GeV. These studies show that the experimental < v2 > has substantial contribution from partonic interactions at \surd sNN = 200 GeV whose magnitude reduces with decrease in beam energy. We also compare the available data on the transverse momentum and pseudorapidity dependence of v2 to those from the above models.

AZIMUTHAL ASYMMETRY AND CORRELATIONS OF HARD PHOTONS IN INTERMEDIATE ENERGY HEAVY ION COLLISIONS

Hard photon emitted from energetic heavy ion collisions is of very interesting since it does not experience the late-stage nuclear interaction, therefore it is useful to explore the early-stage information of matter phase. In this work, we investigated the directed flow and elliptic flow for proton-neutron bremsstrahlung hard photons in intermediate energy heavy-ion collisions. The positive directed flow and negative elliptic flow of directed photons are illustrated and they seem to be anti-correlated to the free proton's flow. Also we calculated the two-photon correlation functions from which the information of photon source was extracted, and while two-photon azimuthal correlations are presented as a good method to extract the elliptic flow parameter v2 of direct hard photons.

Energy dependence of the v2-scaling and the QCD phase boundary

In high-energy nuclear collisions at RHIC ( = 60–200 GeV), quark coalescence has been suggested as one of the processes for hadronization. As a result, one observes a scaling in the elliptic flow parameter v2 and hadron-type dependence (within the 2 < pT < 5 GeV/c region) in the nuclear modification parameter RAA. On the other hand, in a given collision when the center of mass energy is not sufficiently high to create partonic matter, one would not expect the scaling in the final observed v2. Hence, the scaling provides us a sensitive tool for the search for the possible phase boundary in the hot/dense matter dominated by either partonic or hadronic degrees of freedom. In this paper, we will report the results from analyzing the energy dependence of v2 for identified hadrons from Au+Au collisions. Data from transport models are used in our analysis. In this model calculation, without the partonic coalescence the scaling in v2 is absent.

Correlations among elliptic flow parameter, impact parameter, and multiplicity

The elliptic flow parameter, v2, in the Fourier expansion of the event-by-event charged-particle multiplicity azimuthal distribution in the momentum space is studied by taking into account the multiplicity fluctuations. The correlations among measurable variables of v2, charged multiplicity, and impact parameter are investigated using a multiple phase transport model with string melting. It turned out that the charged multiplicity and impact parameter are negatively correlated. This correlation results in the peak structure in v2 as a function of the participant nucleon number (charged multiplicity, impact parameter) measured in RHIC experiments. It is suggested that v2 calculated in the event-wise average is about 20% larger than in the particle-wise average, so event-wise average should be used in the theoretical calculations.

Dependence of elliptic flow on number of parton degrees of freedom

We calculate the elliptic flow parameter $v_2$ for Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV employing the parton cascade BAMPS (Boltzmann Approach of Multiparton Scatterings). Besides gluon interactions including the bremsstrahlung process, interactions with quarks are considered in an effective, but approximate way to investigate the dependence of the collective flow on the number of parton degrees of freedom. We find that $v_2$ as a function of the transverse momentum $p_T$ is sensitive to the number of parton degrees of freedom, whereas the $p_T$ averaged $v_2$ does not. When including quarks, $v_2(p_T)$ shifts to lower $p_T$, the parton transverse momentum spectra become softer and the mean parton transverse momenta decrease.

Event-by-Event Fluctuations of Azimuthal Particle Anisotropy inAu+AuCollisions atsNN=200 GeV

This Letter presents the first measurement of event-by-event fluctuations of the elliptic flow parameter v(2) in Au+Au collisions at square root(s(NN))=200 GeV as a function of collision centrality. The relative nonstatistical fluctuations of the v(2) parameter are found to be approximately 40%. The results, including contributions from event-by-event elliptic flow fluctuations and from azimuthal correlations that are unrelated to the reaction plane (nonflow correlations), establish an upper limit on the magnitude of underlying elliptic flow fluctuations. This limit is consistent with predictions based on spatial fluctuations of the participating nucleons in the initial nuclear overlap region. These results provide important constraints on models of the initial state and hydrodynamic evolution of relativistic heavy ion collisions.

Identification of flow background to subtract in jet-like azimuthal correlations

We derive an analytical form for flow-background to jet-like azimuthal correlation in a cluster approach. We argue that the elliptic flow parameter to use in jet-correlation background is that from two-particle method excluding non-flow correlation unrelated to the reaction plane, but including cross-terms between cluster correlation and cluster flow. We verify our result with Monte Carlo simulations. We discuss implications of our finding in the context of jet-like correlations from STAR and PHENIX.

Formation Time of QGP from Thermal Photon Elliptic Flow

We show that the transverse momentum dependent elliptic flow ν 2 ( p T ) of thermal photons is quite sensitive to the initial formation time ( τ 0 ) of Quark Gluon Plasma (QGP) for semi-central collision of gold nuclei at RHIC [R. Chatterjee and D. K. Srivastava, Phys. Rev. C 79, 021901(R) (2009)]. A smaller value of the formation time or a larger initial temperature leads to a significant increase in the thermal photon radiation from QGP phase, which has a smaller ν 2 . The elliptic flow of thermal photon is dominated by the contribution from the quark matter at intermediate and high p T range and as a result sum ν 2 decreases with smaller τ 0 for p T ⩾ 1.5 GeV . On the other hand we find that the elliptic flow parameter for hadrons depends only marginally on the value of τ 0 .

Elliptic flow of thermal photons inAu+Aucollisions atsNN=200GeV

The transverse momentum $({p}_{t})$ dependence, the centrality dependence, and the rapidity dependence of the elliptic flow of thermal photons in $\mathrm{Au}+\mathrm{Au}$ collisions at $\sqrt{{s}_{\mathit{NN}}}=200$ GeV are predicted on the basis of a three-dimensional ideal hydrodynamic description of the hot and dense matter. The elliptic flow parameter ${v}_{2}$, i.e., the second Fourier coefficient of azimuthal distribution, of thermal photons first increases with ${p}_{t}$ and then decreases for ${p}_{t}&gt;2$ GeV/$c$, because of the weak transverse flow at the early stage. The ${p}_{t}$-integrated ${v}_{2}$ first increases with centrality, reaches a maximum at about 50% centrality, and then decreases. 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 the longitudinal direction, which provides a useful tool to extract the realistic initial condition from measurements.

Hydrodynamic analysis of heavy-ion collisions at the RHIC

Current status of dynamical modeling of relativistic heavy-ion collisions and hydrodynamic description of the quark–gluon plasma is reported. We find the hadronic rescattering effect plays an important role in the interpretation of the mass splitting pattern in the differential elliptic flow data observed at the RHIC. To demonstrate this, we predict the elliptic flow parameter for ϕ mesons to directly observe the flow just after hadronization. We also discuss recent applications of outputs from hydrodynamic calculations to J/ψ suppression, thermal photon radiation and heavy quark diffusion.

Single photons from relativistic collisions of lead nuclei at energies available at the CERN Super Proton Synchrotron (SPS): A reanalysis

We present a reanalysis of single photon production from a relativistic collision of lead nuclei at CERN SPS measured by the WA98 experiment. The refinements include use of isospin and shadowing corrected NLO pQCD treatment for prompt photon production using an optimized scale for factorization, renormalization, and fragmentation and use of hydrodynamics suited for noncentral collisions along with a well tested equation of state admitting a quark-hadron phase transition. A quantitative explanation of the data requires a large initial temperature (at a small formation time of about 0.2 fm/$c$) and a moderate increase in the prompt yield which could perhaps be attributed to the Cronin effect in nuclei. The data can also be explained using a moderate initial temperature (at a formation time of about 1 fm/$c$) with a very large $K$-factor multiplying the prompt yield. We show that different initial times give rise to different values for the elliptic flow parameter ${v}_{2}$ for thermal photons. We also argue that a measurement of ${v}_{2}$ for thermal photons could also distinguish between the scenarios with or without a phase transition.

J/ψ production measurements by the PHENIX experiment

Measurements of J/$\psi$ production by the PHENIX experiment in p+p, d+Au, Cu+Cu and Au+Au collisions at $\sqrt{s_{NN}}$=200 GeV are reviewed. The results show a suppression beyond what can be explained by cold nuclear matter effects in the most central Au+Au and to a lesser extent in Cu+Cu collisions. In addition, the suppression observed at mid rapidity in Au+Au is smaller than at forward rapidity, a tendency opposite to what is expected from the higher energy density at mid rapidity. Regeneration, a possible explanation, can be tested by measuring the elliptic flow parameter v$_2$ of J/$\psi$.

Negative elliptic flow of J/ψ’s: A qualitative signature for charm collectivity at RHIC

We discuss one of the most prominent features of the very recent preliminary elliptic flow data of J/ψ-mesons from the PHENIX Collaboration (PHENIX Collaboration (C. Silvestre), arXiv:0806.0475 [nucl-ex]). Even within the rather large error bars of the measured data a negative elliptic flow parameter (v2) for J/ψ in the range of p T = 0.5-2.5 GeV/c is visible. We argue that this negative elliptic flow at intermediate pT is a clear and qualitative signature for the collectivity of charm quarks produced in nucleus-nucleus reactions at RHIC. Within a parton recombination approach we show that a negative elliptic flow puts a lower limit on the collective transverse velocity of heavy quarks. The numerical value of the transverse flow velocity $ \beta_{T}^{}$ for charm quarks that is necessary to reproduce the data is $ \beta_{T}^{}$ (charm) ∼ 0.55-0.6c and therefore compatible with the flow of light quarks.

A NLO ANALYSIS ON AZIMUTHAL ANISOTROPY OF HIGH pT HADRON IN HEAVY-ION COLLISIONS

The azimuthal anisotropy of high pT hadron in high energy A + A collisions is studied within the next-to-leading order (NLO) perturbative QCD parton model. The effect of jet quenching is incorporated via a model for modified jet fragmentation functions due to radiative parton energy loss in dense medium. Because NLO contributions behave with stronger quenching effect than LO contributions, the NLO elliptic flow parameter is found to be larger than the LO in the medium pT region.

Scaling ofv2in heavy ion collisions

We interpret the scaling of the corrected elliptic flow parameter with respect to the corrected multiplicity, observed to hold in heavy ion collisions for a wide variety of energies and system sizes. We use dimensional analysis and power-counting arguments to place constraints on the changes of initial conditions in systems with different center of mass energy $\sqrt{s}$. Specifically, we show that a large class of changes in the (initial) equation of state, mean free path, and longitudinal geometry over the observed $\sqrt{s}$ are likely to spoil the scaling in ${v}_{2}$ observed experimentally. We therefore argue that the system produced at most Super Proton Synchrotron (SPS) and Relativistic Heavy Ion Collider (RHIC) energies is fundamentally the same as far as the soft and approximately thermalized degrees of freedom are considered. The ``sQGP'' (Strongly interacting Quark-Gluon Plasma) phase, if it is there, is therefore not exclusive to RHIC. We suggest, as a goal for further low-energy heavy ion experiments, to search for a ``transition'' $\sqrt{s}$ where the observed scaling breaks.

AZIMUTHAL ANISOTROPY MEASUREMENT OF DIRECT PHOTON IN $\sqrt{^SNN} = 200\ {\rm GeV}$Au + Au COLLISIONS AT RHIC-PHENIX

Azimuthal anisotropy of direct photons is measured in [Formula: see text] Au + Au collisions by the PHENIX experiment at RHIC. Direct photons are one of the most effective probes to study properties of hot dense medium at initial state (also QGP state) of heavy ion collisions because photons do not interact strongly with medium once produced. They keep their conditions when they are created. Within statistical and systematic errors, the elliptic flow parameter (v2) of direct photons is consistent with zero. Direct photons v2 is measured by the hadron decay photon background v2 from inclusive photon v2 in intermediate to high transverse momentum (pT) region (0 to 10 GeV/c) for 3 centrality selections (20% steps) and minimum bias.

Relativistic Hydrodynamics at RHIC and LHC

Recent development of a hydrodynamic model is discussed by putting an emphasis on realistic treatment of the early and late stages in relativistic heavy ion collisions. The model, which incorporates a hydrodynamic description of the quark-gluon plasma with a kinetic approach of hadron cascades, is applied to analysis of elliptic flow data at the Relativistic Heavy Ion Collider energy. It is predicted that the elliptic flow parameter based on the hybrid model increases with the collision energy up to the Large Hadron Collider energy.

Recent results from the BRAHMS experiment

We present recent results obtained by the BRAHMS experiment at the Relativistic Heavy Ion Collider (RHIC) for the systems of Au+Au and Cu+Cu at s NN = 200 GeV and at 62.4 GeV, and p+p at s NN = 200 GeV . BRAHMS explores reaction dynamics and properties of the hot and high energy density matter produced in ultra-relativistic heavy-ion collisions versus its longitudinal expansion. Overall charged-particle production and particle spectra over a large rapidity interval and p T range are presented. Nuclear modification factors for Au+Au and Cu+Cu collisions are discussed. The observed number of charged particles produced per unit of rapidity in the central rapidity region indicates that a high energy density system is produced at the initial stage of the Au+Au reaction. Analysis of anti-particle to particle ratios as a function of rapidity and collision energy reveal that particle populations at the chemical freeze-out stage for heavy-ion reactions at and above SPS energies are controlled by the baryon chemical potential. From the particle spectra we deduce significant radial expansion ( β ≈ 0.75 ), as expected for systems created with a large initial energy density. We also measure the elliptic flow parameter v 2 versus rapidity and p T . A weak dependence on rapidity of the p T differential v 2 is observed. We present rapidity dependent p / π ratios within 0 y 3 for Au+Au and Cu+Cu at s NN = 200 GeV . The ratios are enhanced in nucleus-nucleus collisions as compared to p+p collisions. The particle ratios are discussed in terms of their system size and rapidity dependence. We compare R AA for Au+Au at s NN = 200 GeV and at 62.4 GeV, and for Au+Au and Cu+Cu at s NN = 200 GeV . R AA is found to increase with decreasing collision energy, decreasing system size, and when going towards more peripheral collisions. However, R AA shows only a very weak dependence on rapidity (for 0 y 3.2 ), both for pions and protons.