Methods for analyzing anisotropic flow in relativistic nuclear collisions

TL;DR

The paper presents a Fourier-based framework to quantify anisotropic flow in relativistic nuclear collisions, relating azimuthal anisotropies to the reaction plane through $v_n$ coefficients. It provides explicit methods to estimate the event plane from sub-events, correct the observed coefficients with the event-plane resolution, and perform both event-by-event and plane-based analyses, including acceptance and non-flow considerations. It discusses non-flow contributions via a parameter $c$, practical Monte Carlo embedding of flow, and extensions to higher harmonics and $p_t$ dependence, as well as the interpretation of pair correlations. Overall, the approach enables robust extraction of flow coefficients across harmonics and energies, facilitating comparisons with hydrodynamic and transport models of collective motion.

Abstract

The strategy and techniques for analyzing anisotropic flow (directed, elliptic, etc.) in relativistic nuclear collisions are presented. The emphasis is on the use of the Fourier expansion of azimuthal distributions. We present formulae relevant for this approach, and in particular, show how the event multiplicity enters into the event plane resolution. We also discuss the role of non-flow correlations and a method for introducing flow into a simulation.

Figures (1)

• Figure 1: The event plane resolution for the $n-$th ($n=km$) harmonic of the particle distribution with respect to the $m-$th harmonic plane, as a function of $\chi_m=v_m/\sigma$.