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We present a new method for analyzing directed and elliptic flow in heavy ion collisions. Unlike standard methods, it separates the contribution of flow to azimuthal correlations from contributions due to other effects. The separation relies on a cumulant expansion of multiparticle azimuthal correlations, and includes corrections for detector inefficiencies. This new method allows the measurement of the flow of identified particles in narrow phase-space regions, and can be used in every regime, from intermediate to ultrarelativistic energies.25.75.Ld 25.75.Gz

In ultrarelativistic heavy-ion collisions, the Fourier decomposition of the relative azimuthal angle, \Delta \phi, distribution of particle pairs yields a large cos(3\Delta \phi) component, extending out to large rapidity separations \Delta \eta >1. This component captures a significant portion of the ridge and shoulder structures in the \Delta \phi distribution, which have been observed after contributions from elliptic flow are subtracted. An average finite triangularity due to event-by-event fluctuations in the initial matter distribution, followed by collective flow, naturally produces a cos(3\Delta \phi) correlation. Using ideal and viscous hydrodynamics, and transport theory, we study the physics of triangular (v_3) flow in comparison to elliptic (v_2), quadrangular (v_4) and pentagonal (v_5) flow. We make quantitative predictions for v_3 at RHIC and LHC as a function of centrality and transverse momentum. Our results for the centrality dependence of v_3 show a quantitative agreement with data extracted from previous correlation measurements by the STAR collaboration. This study supports previous results on the importance of triangular flow in the understanding of ridge and shoulder structures. Triangular flow is found to be a sensitive probe of initial geometry fluctuations and viscosity.Comment: 10 pages, 12 figures. minor changes, and results for $v_5$ added (fig.12

We investigate how the initial geometry of a heavy-ion collision is transformed into final flow observables by solving event-by-event ideal hydrodynamics with realistic fluctuating initial conditions. We study quantitatively to what extent anisotropic flow (v n ) is determined by the initial eccentricity ε n for a set of realistic simulations, and we discuss which definition of ε n gives the best estimator of v n . We find that the common practice of using an r 2 weight in the definition of ε n in general results in a poorer predictor of v n than when using r n weight, for n > 2. We similarly study the importance of additional properties of the initial state. For example, we show that in order to correctly predict v 4 and v 5 for noncentral collisions, one must take into account nonlinear terms proportional to ε 2 2 and ε 2 ε 3 , respectively. We find that it makes no difference whether one calculates the eccentricities over a range of rapidity or in a single slice at z = 0, nor is it important whether one uses an energy or entropy density weight. This knowledge will be important for making a more direct link between experimental observables and hydrodynamic initial conditions, the latter being poorly constrained at present.

The methods currently used to measure azimuthal distributions of particles in heavy ion collisions assume that all azimuthal correlations between particles result from their correlation with the reaction plane. However, other correlations exist, and it is safe to neglect them only if azimuthal anisotropies are much larger than 1/ √ N , with N the total number of particles emitted in the collision. This condition is not satisfied at ultrarelativistic energies. We propose a new method, based on a cumulant expansion of multiparticle azimuthal correlations, which allows measurements of much smaller values of azimuthal anisotropies, down to 1/N . It is simple to implement and can be used to measure both integrated and differential flow. Furthermore, this method automatically eliminates the major systematic errors, which are due to azimuthal asymmetries in the detector acceptance.

We argue that RHIC data, in particular those on the anisotropic flow coefficients v2 and v4, suggest that the matter produced in the early stages of nucleus-nucleus collisions is incompletely thermalized. We interpret the parameter (1/S)(dN/dy), where S is the transverse area of the collision zone and dN/dy the multiplicity density, as an indicator of the number of collisions per particle at the time when elliptic flow is established, and hence as a measure of the degree of equilibration. This number serves as a control parameter which can be varied experimentally by changing the system size, the centrality or the beam energy. We provide predictions for Cu-Cu collisions at RHIC as well as for Pb-Pb collisions at the LHC.

We show that the centrality and system-size dependence of elliptic flow measured at RHIC are fully described by a simple model based on eccentricity scaling and incomplete thermalization. We argue that the elliptic flow is at least 25% below the (ideal) "hydrodynamic limit", even for the most central Au-Au collisions. This lack of perfect equilibration allows for estimates of the effective parton cross section in the Quark-Gluon Plasma and of its viscosity to entropy density ratio. We also show how the initial conditions affect the transport coefficients and thermodynamic quantities extracted from the data, in particular the viscosity and the speed of sound.

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