Flow measurements via two-particle azimuthal correlations in Au + Au collisions at sqrt [s(NN)]=130 GeV

Collision-System and Beam-Energy Dependence of Anisotropic Flow Fluctuations

Elliptic flow measurements from two-, four-, and six-particle correlations are used to investigate flow fluctuations in collisions of U+U at sqrt[s_{NN}]=193  GeV, Cu+Au at sqrt[s_{NN}]=200  GeV and Au+Au spanning the range sqrt[s_{NN}]=11.5-200  GeV. The measurements show a strong dependence of the flow fluctuations on collision centrality, a modest dependence on system size, and very little if any, dependence on particle species and beam energy. The results, when compared to similar LHC measurements, viscous hydrodynamic calculations, and trento model eccentricities, indicate that initial-state-driven fluctuations predominate the flow fluctuations generated in the collisions studied.

From Hydrodynamics to Jet Quenching, Coalescence, and Hadron Cascade: A Coupled Approach to Solving the R_{AA}⊗v_{2} Puzzle

Hydrodynamics and jet quenching are responsible for the elliptic flow v_{2} and suppression of large transverse momentum (p_{T}) hadrons, respectively, two of the most important phenomena leading to the discovery of a strongly coupled quark-gluon plasma in high-energy heavy-ion collisions. A consistent description of the hadron suppression factor R_{AA} and v_{2}, especially at intermediate p_{T}, however, remains a challenge. We solve this long-standing R_{AA}⊗v_{2} puzzle by including quark coalescence for hadronization and final state hadron cascade in the coupled linear Boltzmann transport-hydro model that combines concurrent jet transport and hydrodynamic evolution of the bulk medium. We illustrate that quark coalescence and hadron cascade, two keys to solving the puzzle, also lead to a splitting of v_{2} for pions, kaons, and protons in the intermediate p_{T} region. We demonstrate for the first time that experimental data on R_{AA}, v_{2}, and their hadron flavor dependence from low to intermediate and high p_{T} in high-energy heavy-ion collisions can be understood within this coupled framework.

Azimuthal Harmonics in Small and Large Collision Systems at RHIC Top Energies

The first (v_{1}^{fluc}), second (v_{2}), and third (v_{3}) harmonic coefficients of the azimuthal particle distribution at midrapidity are extracted for charged hadrons and studied as a function of transverse momentum (p_{T}) and mean charged particle multiplicity density ⟨N_{ch}⟩ in U+U (sqrt[s_{NN}]=193  GeV), Au+Au, Cu+Au, Cu+Cu, d+Au, and p+Au collisions at sqrt[s_{NN}]=200  GeV with the STAR detector. For the same ⟨N_{ch}⟩, the v_{1}^{fluc} and v_{3} coefficients are observed to be independent of the collision system, while v_{2} exhibits such a scaling only when normalized by the initial-state eccentricity (ϵ_{2}). The data also show that ln(v_{2}/ϵ_{2}) scales linearly with ⟨N_{ch}⟩^{-1/3}. These measurements provide insight into initial-geometry fluctuations and the role of viscous hydrodynamic attenuation on v_{n} from small to large collision systems.

Recent ATLAS measurements of azimuthal anisotropies in pp and p+Pb collisions

The azimuthal anisotropies of particle yields observed in relativistic heavy-ion collisions are considered as an evidence of the formation on a deconfined Quark-Gluon Plasma produced in these collisions. Interestingly, recent measurements in pp and p+Pb systems from ATLAS and other experiments show similar features as those observed in A+A collisions, indicating the possibility of the production of such a deconfined medium in smaller collision systems. This report presents a summary of the recent ATLAS results on azimuthal anisotropies in pp collisions at 5.02 TeV and 13 TeV, p+Pb collisions at 5.02 TeV and 8.16 TeV as well as in peripheral 2.76 TeV Pb+Pb interactions. It includes measurements of two-particle correlations of charged particles as well as correlations of heavy flavor muons and charged particles in Δϕ and Δη, with a template fitting procedure used to subtract the dijet contributions. Additionally, measurements of cumulants of multi-particle correlations, cn{2-8} are presented. The two-particle correlations and cumulants confirm a presence of collective phenomena in these collision systems, but the results on four-particle cumulants for pp collisions do not demonstrate a similar collective behaviour. However, the cumulant measurements in small collision systems can be biased by non-flow correlations. A novel subevent cumulant method that suppresses the contribution of non-flow effects was proposed recently by ATLAS allowing to measure significant azimuthal anisotropies in both pp and p+Pb collisions.

Sub-leading flow modes in PbPb collisions at √sNN =2.76 TeV from HYDJET++ model

The LHC results on the sub-leading flow modes in PbPb collisions at 2.76 TeV, related to initial-state fluctuations, are analyzed and interpreted within the HYDJET++ model. Using the newly introduced Principal Component Analysis (PCA) method applied to two-particle azimuthal correlations extracted from the model calculations, the leading and the sub-leading flow modes are studied as a function of the transverse momentum (pT ) over a wide centrality range. The leading modes of the elliptic (v(1)2) and triangular (v3(1)3) flow calculated within the HYDJET++ model reproduce rather well the v2{2} and v3{2} coeffcients experimentally measured using the two-particle correlations. Within the pT ≤3 GeV/c range where hydrodynamics dominates, the sub-leading flow effects are greatest at the highest pT of around 3 GeV/c. The sub-leading elliptic flow mode (v2(2)), which corresponds to n=2 harmonic, has a small non-zero value and slowly increases from central to peripheral collisions, while the sub-leading triangular flow mode (v3(2)), which corresponds to n =3 harmonic, is even smaller and does not depend on centrality. For n =2, the relative magnitude of the effect measured with respect to the leading flow mode shows a shallow minimum for semi-central collisions and increases for very central and for peripheral collisions. For n =3 case, there is no centrality dependence. The subleading flow mode results obtained from the HYDJET++ model are in a rather good agreement with the experimental measurements of the CMS Collaboration.

Measurement of multi-particle azimuthal correlations in pp, p + Pb and low-multiplicity Pb + Pb collisions with the ATLAS detector

Multi-particle cumulants and corresponding Fourier harmonics are measured for azimuthal angle distributions of charged particles in [Formula: see text] collisions at [Formula: see text] = 5.02 and 13 TeV and in [Formula: see text] + Pb collisions at [Formula: see text] = 5.02 TeV, and compared to the results obtained for low-multiplicity [Formula: see text] collisions at [Formula: see text] = 2.76 TeV. These measurements aim to assess the collective nature of particle production. The measurements of multi-particle cumulants confirm the evidence for collective phenomena in [Formula: see text] + Pb and low-multiplicity [Formula: see text] collisions. On the other hand, the [Formula: see text] results for four-particle cumulants do not demonstrate collective behaviour, indicating that they may be biased by contributions from non-flow correlations. A comparison of multi-particle cumulants and derived Fourier harmonics across different collision systems is presented as a function of the charged-particle multiplicity. For a given multiplicity, the measured Fourier harmonics are largest in [Formula: see text], smaller in [Formula: see text] + Pb and smallest in [Formula: see text] collisions. The [Formula: see text] results show no dependence on the collision energy, nor on the multiplicity.

Directed flow of charged particles at midrapidity relative to the spectator plane in Pb-Pb collisions at √(s(NN))=2.76 TeV

The directed flow of charged particles at midrapidity is measured in Pb-Pb collisions at √(s(NN))=2.76 TeV relative to the collision symmetry plane defined by the spectator nucleons. A negative slope of the rapidity-odd directed flow component with approximately 3 times smaller magnitude than found at the highest RHIC energy is observed. This suggests a smaller longitudinal tilt of the initial system and disfavors the strong fireball rotation predicted for the LHC energies. The rapidity-even directed flow component is measured for the first time with spectators and found to be independent of pseudorapidity with a sign change at transverse momenta p(T) between 1.2 and 1.7  GeV/c. Combined with the observation of a vanishing rapidity-even p(T) shift along the spectator deflection this is strong evidence for dipolelike initial density fluctuations in the overlap zone of the nuclei. Similar trends in the rapidity-even directed flow and the estimate from two-particle correlations at midrapidity, which is larger by about a factor of 40, indicate a weak correlation between fluctuating participant and spectator symmetry planes. These observations open new possibilities for investigation of the initial conditions in heavy-ion collisions with spectator nucleons.

Directed flow at midrapidity in sqrt[S(NN)] = 2.76 TeV Pb + Pb collisions

We analyze published data from the ALICE Collaboration in order to obtain the first extraction of the recently proposed rapidity-even directed flow observable v(1). An accounting of the correlation due to the conservation of transverse momentum restores the factorization seen by ALICE in all other Fourier harmonics and thus indicates that the remaining correlation gives a reliable measurement of directed flow. We then carry out the first viscous hydrodynamic calculation of directed flow, and show that it is less sensitive to viscosity than higher harmonics. This allows for a direct extraction of the dipole asymmetry of the initial state, providing a strict constraint on the nonequilibrium dynamics of the early-time system. A prediction is then made for v(1) in Au-Au collisions at RHIC.

Elliptic flow for phi mesons and (anti)deuterons in Au+Au collisions at square root of sNN=200 GeV

Differential elliptic flow (v(2)) for phi mesons and (anti)deuterons (d)d is measured for Au+Au collisions at square root of sNN=200 GeV. The v(2) for phi mesons follows the trend of lighter pi+/- and K+/- mesons, suggesting that ordinary hadrons interacting with standard hadronic cross sections are not the primary driver for elliptic flow development. The v(2) values for (d)d suggest that elliptic flow is additive for composite particles. This further validation of the universal scaling of v(2) per constituent quark for baryons and mesons suggests that partonic collectivity dominates the transverse expansion dynamics.

Scaling properties of azimuthal anisotropy in Au+Au and Cu+Cu Collisions at sqrt[s NN]=200 GeV

Differential measurements of elliptic flow (v2) for Au+Au and Cu+Cu collisions at sqrt[sNN]=200 GeV are used to test and validate predictions from perfect fluid hydrodynamics for scaling of v2 with eccentricity, system size, and transverse kinetic energy (KE T). For KE T identical with mT-m up to approximately 1 GeV the scaling is compatible with hydrodynamic expansion of a thermalized fluid. For large values of KE T mesons and baryons scale separately. Quark number scaling reveals a universal scaling of v2 for both mesons and baryons over the full KE T range for Au+Au. For Au+Au and Cu+Cu the scaling is more pronounced in terms of KE T, rather than transverse momentum.

Elliptic flow of thermal photons in relativistic nuclear collisions

We predict the transverse momentum (p(T)) dependence of elliptic flow of thermal photons for Au + Au collisions at the BNL Relativistic Heavy Ion Collider. We model the system hydrodynamically, with a thermalized quark-gluon plasma at early times followed by hadronization and decoupling. Photons are emitted throughout the expansion history. Contrary to hadron elliptic flow, which increases monotonically with p(T), the elliptic flow nu2(p(T)) of thermal photons is predicted to first rise and then fall again. Photon elliptic flow at high p(T) reflects the quark momentum anisotropy at early times when it is small, while at low p(T) it mirrors the large pion momentum anisotropy during the late hadronic emission stage. An interesting structure is predicted at intermediate p(T) approximately 0.4 GeV/c, where photon elliptic flow reflects the momenta and the (compared to pions) reduced nu2 of heavy vector mesons in the late hadronic phase.

Saturation of azimuthal anisotropy in Au + Au collisions at (square root)s(NN) = 62-200 GeV

New measurements are presented for charged hadron azimuthal correlations at midrapidity in Au+Au collisions at (square root)s(NN) = 62.4 and 200 GeV. They are compared to earlier measurements obtained at (square root)s(NN) = 130 GeV and in Pb + Pb collisions at (square root)s(NN) = 17.2 GeV. Sizeable anisotropies are observed with centrality and transverse momentum (pT) dependence characteristic of elliptic flow (upsilon2). For a broad range of centralities, the observed magnitudes and trends of the differential anisotropy, upsilon2(pT), change very little over the collision energy range (square root)s(NN) = 62-200 GeV, indicating saturation of the excitation function for upsilon2 at these energies. Such a saturation may be indicative of the dominance of a very soft equation of state for (square root)s(NN) approximately 60-200 GeV.

Equation of state of gluon plasma from a fundamental modular region

Despite considerable practical success in dealing with the gluon plasma, finite-temperature perturbation theory suffers at the fundamental level from infrared divergences discovered by Linde. However, if gauge or Gribov copies are properly eliminated from the physical state space, infrared modes are strongly suppressed. We describe the gluon plasma in zeroth order as a gas of free quasiparticles with a temperature-independent dispersion relation of Gribov type, E(k)=k(2)sqrt[+M4 / k(2)], that results from the reduction of the physical state space. The effective mass M2 / k controls infrared divergences and allows finite calculable corrections. The equation of state of this gas is calculated and compared with numerical lattice data.

Measuring the collective flow with jets

In nucleus-nucleus collisions, high-p(T) partons interact with a dense medium, which possesses strong collective flow components. Here, we demonstrate that the resulting medium-induced gluon radiation does not depend solely on the energy density of the medium, but also on the collective flow. Both components can be disentangled by the measurement of particle production associated with high-p(T) trigger particles, jetlike correlations, and jets. In particular, we show that flow effects lead to a characteristic breaking of the rotational symmetry of the average jet energy and jet multiplicity distribution in the eta x phi plane. We argue that data on the medium-induced broadening of jetlike particle correlations in Au + Au collisions at the Relativistic Heavy-Ion Collider may provide evidence for a significant distortion of parton fragmentation due to the longitudinal collective flow.

Measurement of nonrandom event-by-event fluctuations of average transverse momentum in square root of (sNN)=200 GeV Au+Au and p+p collisions

Event-by-event fluctuations of the average transverse momentum of produced particles near midrapidity have been measured by the PHENIX Collaboration in square root of (sNN)=200 GeV Au+Au, and p+p collisions at the Relativistic Heavy Ion Collider. The fluctuations are observed to be in excess of the expectation for statistically independent particle emission for all centralities. The excess fluctuations exhibit a dependence on both the centrality of the collision and on the pT range over which the average is calculated. Both the centrality and pT dependence can be well reproduced by a simulation of random particle production with the addition of contributions from hard-scattering processes.

Azimuthal anisotropy at the relativistic heavy ion collider: the first and fourth harmonics

We report the first observations of the first harmonic (directed flow, v(1)) and the fourth harmonic (v(4)), in the azimuthal distribution of particles with respect to the reaction plane in Au+Au collisions at the BNL Relativistic Heavy Ion Collider (RHIC). Both measurements were done taking advantage of the large elliptic flow (v(2)) generated at RHIC. From the correlation of v(2) with v(1) it is determined that v(2) is positive, or in-plane. The integrated v(4) is about a factor of 10 smaller than v(2). For the sixth (v(6)) and eighth (v(8)) harmonics upper limits on the magnitudes are reported.

Differential freeze-out and pion interferometry at RHIC from covariant transport theory

Puzzling discrepancies between recent pion interferometry data on Au+Au reactions at square root of s=30 and 200 AGeV from RHIC and predictions based on ideal hydrodynamics are analyzed in terms of covariant parton transport theory. The discrepancies in the R(out)/R(side) ratio are significantly reduced when the finite opacity of the gluon plasma is taken into account. However, the magnitude of the radii is not well accounted for.

Semihard scattering unraveled from collective dynamics by two-pion azimuthal correlations in 158A GeV/c Pb+Au collisions

Elliptic flow and two-particle azimuthal correlations of charged hadrons and high-p(T) pions (p(T)>1 GeV/c) have been measured close to midrapidity in 158A GeV/c Pb+Au collisions by the CERES experiment. Elliptic flow (v(2)) rises linearly with p(T) to a value of about 10% at 2 GeV/c. Beyond p(T) approximately 1.5 GeV/c, the slope decreases considerably, possibly indicating a saturation of v(2) at high p(T). Two-pion azimuthal anisotropies for p(T)>1.2 GeV/c exceed the elliptic flow values by about 60% in midcentral collisions. These nonflow contributions are attributed to nearside and back-to-back jetlike correlations, the latter exhibiting centrality dependent broadening.

Elliptic flow of identified hadrons in Au+Au collisions at sqrt sNN =200 GeV

The anisotropy parameter (v(2)), the second harmonic of the azimuthal particle distribution, has been measured with the PHENIX detector in Au+Au collisions at sqrt[s(NN)]=200 GeV for identified and inclusive charged particle production at central rapidities (|eta|<0.35) with respect to the reaction plane defined at high rapidities (|eta|=3-4 ). We observe that the v(2) of mesons falls below that of (anti)baryons for p(T)>2 GeV/c, in marked contrast to the predictions of a hydrodynamical model. A quark-coalescence model is also investigated.

Elliptic flow at large transverse momenta from quark coalescence

We show that hadronization via quark coalescence enhances hadron elliptic flow at large p(perpendicular) relative to that of partons at the same transverse momentum. Therefore, compared to earlier results based on covariant parton transport theory, more moderate initial parton densities dN/deta(b=0) approximately 1500-3000 can explain the differential elliptic flow v(2)(p(perpendicular)) data for Au+Au reactions at sqrt[s]=130 and 200A GeV from BNL RHIC. In addition, v(2)(p(perpendicular)) could saturate at about 50% higher values for baryons than for mesons. If strange quarks have weaker flow than light quarks, hadron v(2) at high p(perpendicular) decreases with relative strangeness content.