No Arabic abstract
The event-plane method, which is widely used to analyze anisotropic flow in nucleus-nucleus collisions, is known to be biased by nonflow effects,especially at high $p_t$. Various methods (cumulants, Lee-Yang zeroes) have been proposed to eliminate nonflow effects, but their implementation is tedious, which has limited their application so far. In this paper, we show that the Lee-Yang-zeroes method can be recast in a form similar to the standard event-plane analysis. Nonflow correlations are strongly suppressed by using the information from the length of the flow vector, in addition to the event-plane angle. This opens the way to improved analyses of elliptic flow and azimuthally-sensitive observables at RHIC and LHC.
The cumulant method is applied to study elliptic flow ($v_2$) in Au+Au collisions at $sqrt{s}=200$AGeV, with the UrQMD model. In this approach, the true event plane is known and both the non-flow effects and event-by-event spatial ($epsilon$) and $v_2$ fluctuations exist. Qualitatively, the hierarchy of $v_2$s from two, four and six-particle cumulants is consistent with the STAR data, however, the magnitude of $v_2$ in the UrQMD model is only 60% of the data. We find that the four and six-particle cumulants are good measures of the real elliptic flow over a wide range of centralities except for the most central and very peripheral events. There the cumulant method is affected by the $v_2$ fluctuations. In mid-central collisions, the four and six-particle cumulants are shown to give a good estimation of the true differential $v_2$, especially at large transverse momentum, where the two-particle cumulant method is heavily affected by the non-flow effects.
We discuss how the different estimates of elliptic flow are influenced by flow fluctuations and nonflow effects. It is explained why the event-plane method yields estimates between the two-particle correlation methods and the multiparticle correlation methods. It is argued that nonflow effects and fluctuations cannot be disentangled without other assumptions. However, we provide equations where, with reasonable assumptions about fluctuations and nonflow, all measured values of elliptic flow converge to a unique mean v_{2,PP} elliptic flow in the participant plane and, with a Gaussian assumption on eccentricity fluctuations, can be converted to the mean v_{2,RP} in the reaction plane. Thus, the 20% spread in observed elliptic flow measurements from different analysis methods is no longer mysterious.
The directed flow of particles produced in ultrarelativistic heavy ion collisions at SPS and RHIC is so small that currently available methods of analysis are at the border of applicability. Standard two-particle and flow-vector methods are biased by large nonflow correlations. On the other hand, cumulants of four-particle correlations, which are free from this bias, are plagued by large statistical errors. Here, we present a new method based on three-particle correlations, which uses the property that elliptic flow is large at these energies. This method may also be useful at intermediate energies, near the balance energy where directed flow vanishes.
Centrality dependence of the directed flow of protons in Au+Au collisions at the beam energy of 1.23A GeV collected by the HADES experiment at GSI is presented. Measurements are performed with respect to the spectators plane estimated using the Forward Wall hodoscope. Biases due to non-flow correlations and correlated detector effects are evaluated. The corresponding systematic uncertainties are quantified using estimates of the spectators plane from various forward rapidity regions constructed from groups of Forward Wall channels and protons reconstructed with the HADES tracking system.
This short overview includes recent results from the ALICE Collaboration on anisotropic flow of charged and identified particles in sqrt(sNN) = 2.76 TeV Pb-Pb collisions. We also discuss charge dependent and event plane dependent azimuthal correlations that are important in tests of the chiral magnetic effect, as well as understanding the dynamics of the system evolution and hadronization process. Lastly, we present ALICE results obtained with a new technique, the event shape engineering, which allows to perform a physical analysis on events with very large or small flow.