Correlation Functions and Cumulants in Elliptic Flow Analysis

摘要

We consider various methods of flow analysis in heavy ion collisions and compare experimental data on corresponding observables to the predictions of our saturation model proposed earlier. We demonstrate that, due to the nature of the standard flow analysis, azimuthal distribution of particles with respect to reaction plane determined from the second order harmonics should always be proportional to $\cos 2(\phi-\Psi_R)$ independent of the physical origin of particle correlations (flow or non-flow). The amplitude of this distribution is always physical and proportional to $v_2$. Two-particle correlations analysis is therefore a more reliable way of extracting the shape of physical azimuthal anisotropy. We demonstrate that two-particle correlation functions generated in our minijet model of particle production are in good agreement with the data reported by PHENIX. We discuss the role of non-flow correlations in the cumulant flow analysis and demonstrate using a simple example that if the flow is weak, higher order cumulants analysis does not significantly reduce the contribution of non-flow correlations to elliptic flow observable $v_2$ in RHIC data.