Understanding the correlation between elliptic and triangular flow

TL;DR

This paper investigates the complex relationship between elliptic and triangular flow in nucleus-nucleus collisions, revealing how initial-state fluctuations and impact parameter fluctuations influence their correlation, with findings supported by experimental data and simulations.

Contribution

It introduces a new measure of initial-state skewness and demonstrates its role in explaining the non-monotonic correlation between $v_2$ and $v_3$ in heavy-ion collisions.

Findings

Correlation between $v_2$ and $v_3$ changes sign with centrality.

Initial-state skewness is quantified and linked to experimental data.

Theoretical predictions align with measurements using different centrality classifiers.

Abstract

The relative correlation between the magnitudes of elliptic flow ($v_2$) and triangular flow ($v_3$) has been accurately measured in nucleus-nucleus collisions at the LHC collider. As a function of the centrality of the collision, it changes sign and varies non-monotonically. We show that this is naturally explained by two combined effects. The first effect is a skewness in initial-state fluctuations, which is quantified by the correlation between the geometry-driven elliptic deformation in the reaction plane and the fluctuation-driven triangularity $\varepsilon_3$. We introduce an intensive measure of this skewness, which is generically of order unity and depends weakly on the system size and centrality. We evaluate its magnitude using Monte Carlo simulations of the initial state, which show that it is sensitive to the nucleon width. The second effect is the fluctuation of impact parameter relative to centrality classifiers used by experiment. The ATLAS collaboration uses two different centrality classifiers, the multiplicity $N_{ch}$ and the transverse energy $E_T$. We fit both sets of results for Pb+Pb collisions up to $\approx 40\%$ centrality with a single parameter, the intensive mixed skewness. Its value inferred from experiment agrees with theoretical expectations.