Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions

Abstract

We propose a new method to study transverse ow eects in relativistic nuclear collisions by F ourier analysis of the azimuthal distribution on an eventby-event basis in relatively narrow rapidity windows. The distributions of Fourier coecients provide direct information on the magnitude and type of ow. Directivity and two dimensional sphericity tensor, widely used to analyze ow, emerge naturally in our approach, since they correspond to the distributions of the rst and second harmonic coecients, respectively. The role of nite particle uctuations and particle correlations is discussed.

Anisotropic flow from Lee–Yang zeros: a practical guide

“…It is commonly characterized by the Fourier coefficients of the single-particle distribution [1] v n ≡ cos(n(φ − Φ R )) ,…”

Flow and correlation phenomena measurements in pp, pPb and PbPb collisions at CMS

“…The single-particle azimuthal anisotropy Fourier coefficients v n can then be extracted as v n = √ V n∆ , assuming that factorization applies [12]. The SC technique was first introduced by the ALICE collaboration [5] in LHC measurements and is based on a 4-particle correlation calculations with cumulants.…”

Higher harmonic anisotropic flow of identified particles in Pb–Pb collisions with the ALICE detector

“…In this analysis, the contribution from non-flow was estimated using the HIJING event generator and is denoted as δ MC [6]. The maximum magnitude of this correction is around 0.017 for v 2 , 0.008 for v 3 …”

“…This momentum anisotropy stems from the initial spatial anisotropy of the collision, reflected in its geometry, and by the initial density profile of nucleons participating in the collision which is different from one event to the other [2]. Anisotropic flow is characterized by a Fourier expansion of the azimuthal distribution of particle production relative to the symmetry plane [3], according to:…”