$v_4$, $v_5$, $v_6$, $v_7$: nonlinear hydrodynamic response versus LHC data

TL;DR

This paper investigates the nonlinear hydrodynamic response in heavy-ion collisions by analyzing higher harmonic flow coefficients and their relation to event-plane correlations, providing new insights and predictions for LHC data.

Contribution

It introduces a method to isolate linear and nonlinear flow responses and compares experimental data with hydrodynamic calculations, offering new predictions for $v_7$ at the LHC.

Findings

CMS and ATLAS data on $v_4$ and $v_6$ are compatible.

Experimental data on $v_4$, $v_5$, and $v_6$ agree with hydrodynamic models.

Predictions for $v_7$ versus centrality in Pb-Pb collisions are provided.

Abstract

Higher harmonics of anisotropic flow ($v_n$ with $n\ge 4$) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. We explain how such measurements are related to event-plane correlations. We show that CMS data on $v_4$ and $v_6$ are compatible with ATLAS data on event-plane correlations. If one assumes that higher harmonics are the superposition of non-linear and linear responses, then the linear and non-linear parts can be isolated under fairly general assumptions. By combining analyses of higher harmonics with analyses of $v_2$ and $v_3$, one can eliminate the uncertainty from initial conditions and define quantities that only involve nonlinear hydrodynamic response coefficients. Experimental data on $v_4$, $v_5$ and $v_6$ are in good agreement with hydrodynamic calculations. We argue that $v_7$ can be measured with respect to elliptic and triangular flow. We present predictions for $v_7$ versus centrality in Pb-Pb collisions at the LHC.