Left-right splitting of elliptic flow due to directed flow in heavy ion collisions

TL;DR

This paper demonstrates that the observed left-right splitting of elliptic flow in heavy ion collisions is primarily caused by directed flow, with confirmation from a multi-phase transport model, and explores its dependencies on various collision parameters.

Contribution

It reveals that the elliptic flow splitting is driven by directed flow and confirms this through a multi-phase transport model, providing analytical and numerical insights.

Findings

Elliptic flow splitting is mainly due to directed flow $v_1$.

The splitting vanishes at zero transverse momentum.

Splitting depends on $p_T$, centrality, energy, and hadron species.

Abstract

Recently the splitting of elliptic flow $v_2$ at finite rapidities has been proposed as a result of the global vorticity in non-central relativistic heavy ion collisions. In this study, we find that this left-right (i.e., on opposite sides of the impact parameter axis) splitting of the elliptic flow at finite rapidities is a result of the non-zero directed flow $v_1$, with the splitting magnitude $\approx 8v_1(1-3v_2)/(3\pi)$. We also use a multi-phase transport model, which automatically includes the vorticity field and flow fluctuations, to confirm the $v_2$ splitting. In addition, we find that the analytical expectations for the $v_2$ splitting work for the raw $v_2$ and $v_1$ (i.e., before event plane resolutions are applied) measured relative to either the first- or second-order event plane. Since the $v_2$ splitting is mostly driven by $v_1$, it vanishes at zero transverse momentum ($p_{\rm T}$), and its magnitude and sign may have non-trivial dependencies on $p_{\rm T}$, centrality, collision energy, and hadron species.