Eccentricities, fluctuations and A-dependence of elliptic and triangular flows in heavy-ion collisions

TL;DR

This paper introduces a simple geometrical model with fluctuations to analyze elliptic and triangular flow in heavy-ion collisions, successfully matching experimental data and revealing the different origins of flow harmonics.

Contribution

The paper presents a new geometrical model incorporating event-by-event fluctuations to describe flow harmonics in heavy-ion collisions, highlighting the different roles of initial geometry and fluctuations.

Findings

Eccentricity $ ext{ε}_3$ is purely fluctuation-driven and depends on overlap size.

Elliptic flow $v_2$ is mainly related to average collision geometry.

Triangular flow $v_3$ is primarily determined by fluctuations.

Abstract

A simple geometrical model with event-by-event fluctuations is suggested to study elliptical and triangular eccentricities in the initial state of relativistic heavy-ion collisions. This model describes rather well the ALICE and ATLAS data for Pb+Pb collisions at center-of-mass energy $\sqrt{s_{NN}} = 5.02$~TeV per nucleon pair, assuming that the second, $v_2$, and third, $v_3$, harmonics of the anisotropic flow are simply linearly proportional to the eccentricities $\varepsilon_2$ and $\varepsilon_3$, respectively. We show that the eccentricity $\varepsilon_3$ has a pure fluctuation origin and is substantially dependent on the size of the overlap area only, while the eccentricity $\varepsilon_2$ is mainly related to the average collision geometry. Elliptic flow, therefore, is weakly dependent on the event-by-event fluctuations everywhere except of the very central collisions 0--2%, whereas triangular flow is mostly determined by the fluctuations. The scaling dependence of the magnitude of the flow harmonics on atomic number, $v_n \propto A^{-1/3}$, is predicted for this centrality interval.