We introduce a cumulant expansion to parameterize possible initial conditions in relativistic heavy ion collisions. We show that the cumulant expansion converges and that it can systematically reproduce the results of Glauber type initial conditions. At third order in the gradient expansion, the cumulants characterize the triangularity r 3 cos 3(φ − ψ 3,3 ) and the dipole asymmetry r 3 cos(φ − ψ 1,3 ) of the initial entropy distribution. We show that for mid-peripheral collisions the orientation angle of the dipole asymmetry ψ 1,3 has a 20% preference out of plane. This leads to a small net v 1 out of plane. In peripheral and mid-central collisions the orientation angles ψ 1,3 and ψ 3,3 are strongly correlated, but this correlation disappears towards central collisions. We study the ideal hydrodynamic response to these cumulants and determine the associated v 1 / 1 and v 3 / 3 for a massless ideal gas equation of state. The space time development of v 1 and v 3 is clarified with figures. These figures show that v 1 and v 3 develop towards the edge of the nucleus, and consequently the final spectra are more sensitive to the viscous dynamics of freezeout. The hydrodynamic calculations for v 3 are provisionally compared to Alver and Roland fit of STAR inclusive two particle correlation functions. Finally, we propose to measure the v 1 associated with the dipole asymmetry and the correlations between ψ 1,3 and ψ 3,3 by measuring a two particle correlation with respect to the participant plane, cos(φ α − 3φ β + 2Ψ P P ) . The hydrodynamic prediction for this correlation function is several times larger than a correlation currently measured by the STAR collaboration, cos(φ α + φ β − 2Ψ P P ) . This experimental measurement would provide convincing evidence for the hydrodynamic and geometric interpretation of two particle correlations at RHIC.

We determine the non-linear hydrodynamic response to geometrical fluctuations in heavy ion collisions using ideal and viscous hydrodynamics. This response is characterized with a set of nonlinear response coefficients that determine, for example, the v 5 that is produced by an 2 and an 3 . We analyze how viscosity damps both the linear and non-linear response coefficients, and provide an analytical estimate that qualitatively explains most of the trends observed in more complete simulations. Subsequently, we use these non-linear response coefficients to determine the linear and non-linear contributions to v 1 , v 4 and v 5 . For viscous hydrodynamics the non-linear contribution is dominant for v 4 , v 5 and higher harmonics. For v 1 , the non-linear response constitutes an important ∼ 25% correction in mid-central collisions. The non-linear response is also analyzed as a function of transverse momentum for v 1 , v 4 and v 5 . Finally, recent measurements of correlations between event-planes of different harmonic orders are discussed in the context of non-linear response. *

We study J/ψ production at RHIC and LHC energies with both initial production and regeneration. We solve the coupled set of transport equation for the J/ψ distribution in phase space and the hydrodynamic equation for evolution of quark-gluon plasma. At RHIC, continuous regeneration is crucial for the J/ψ momentum distribution while the elliptic flow is still dominated by initial production. At LHC energy, almost all the initially created J/ψs are dissociated in the medium and regeneration dominates the J/ψ properties. 12.38.Mh, 24.85.+p The goal of high-energy nuclear collisions is to identify and study the equation of state of the Quark-Gluon Plasma (QGP) which is believed to exist at the early stage of our universe [1]. In √ s N N = 200 GeV Au + Au collisions, the observations of jet-quenching [2] and collective flow have demonstrated the formation of hot and dense matter with partonic collectivity [3,4]. Local thermalization of the system created in heavy ion collisions is yet to be tested. Heavy flavors including charm and bottom quarks are powerful tools [5] for studying the early collision dynamics because their masses are much larger than possible excitation, temperature for example, of the system created in collisions at RHIC. Recent results have shown that heavy flavors are all produced in the initial collisions [6,7]. Therefore, studying open charm and charmonium production will yield important information on the properties of QGP. The J/ψ is a particularly sensitive probe of the early stages because its survial probability depends on the environment. Lattice gauge theory calculations have indicated that J/ψs do exist above the critical temperature [8,9].The J/ψ suppression was first proposed as a direct signature to identify the QGP formation twenty years ago [10]. Besides the normal suppression induced by nuclear absorption, the J/ψs initially produced by hard processes are anomalously suppressed [11,12,13,14,15,16,17] by interactions in the hot medium. While charm quark production at the SPS is expected to be small, there are more than 10 cc pairs produced in a central Au + Au collision at RHIC, and is probably more than 200 pairs at the LHC [18]. These uncorrelated charm quark pairs in the QGP can be recombined to form J/ψs. Obviously, regeneration will enhance the J/ψ yield and alter its momentum spectra. Recently, the regeneration approach for J/ψ production at RHIC has been widely discussed with different models, such as thermal production on the hadronizaton hypersurface according to statistic law [19,20,21], the coalescence mechanism [22] and the kinetic model [23,24] which considers continuous J/ψ regeneration in a QGP.The medium created in high-energy nuclear collisions evolves dynamically. In order to extract information about the medium by analyzing the J/ψ distributions, both the hot and dense medium and the J/ψ production processes must be treated dynamically. In this Letter, we treat continuous regeneration of the J/ψ in a QGP self-consistently, including hydrodynamic evolution of t...

Higher harmonics of anisotropic flow (v n with n ≥ 4) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. We explain how such measurements are related to event-plane correlations. We show that CMS data on v 4 and v 6 are compatible with ATLAS data on event-plane correlations. If one assumes that higher harmonics are the superposition of non-linear and linear responses, then the linear and non-linear parts can be isolated under fairly general assumptions. By combining analyses of higher harmonics with analyses of v 2 and v 3 , one can eliminate the uncertainty from initial conditions and define quantities that only involve nonlinear hydrodynamic response coefficients. Experimental data on v 4 , v 5 and v 6 are in good agreement with hydrodynamic calculations. We argue that v 7 can be measured with respect to elliptic and triangular flow. We present predictions for v 7 versus centrality in Pb-Pb collisions at the LHC.