Nonlinear coupling of flow harmonics: Hexagonal flow and beyond

Abstract

Higher Fourier harmonics of anisotropic flow ($v_4$ and beyond) get large contributions induced by elliptic and triangular flow through nonlinear response. We present a general framework of nonlinear hydrodynamic response which encompasses the existing one, and allows to take into account the mutual correlation between the nonlinear couplings affecting Fourier harmonics of any order. Using Large Hadron Collider data on Pb+Pb collisions at ~$\sqrt[]{s}=2.76$ TeV, we perform an application of our formalism to hexagonal flow, $v_6$, a coefficient affected by several nonlinear contributions which are of the same order of magnitude. We obtain the first experimental measure of the coefficient ${\chi }_{624}$, which couples $v_6$ to $v_2$ and $v_4$. This is achieved by putting together the information from several analyses: event-plane correlations, symmetric cumulants, as well as new higher-order moments recently analyzed by the ALICE collaboration. The value of ${\chi }_{624}$ extracted from data is in fair agreement with hydrodynamic calculations, although with large error bars, which would be dramatically reduced by a dedicated analysis. We argue that within our formalism the nonlinear structure of a given higher harmonic can be determined more accurately than the harmonic itself, and we emphasize potential applications to future measurements of $v_7$ and $v_8$.

arXiv comment9 pages; 5 figures; the Mathematica notebook provided as ancillary file contains a step-by-step analysis of experimental data, with the derivation of all the quantities shown in the paper

References in corpus (31)

• Viscosity in Strongly Interacting Quantum Field Theories from Black Hole Physics
• The Chiral Magnetic Effect
• Collective flow and viscosity in relativistic heavy-ion collisions
• Flow Study in Relativistic Nuclear Collisions by Fourier Expansion of Azimuthal Particle Distributions
• Conformal Relativistic Viscous Hydrodynamics: Applications to RHIC results at sqrt(s_NN) = 200 GeV
• The Effect of Shear Viscosity on Spectra, Elliptic Flow, and HBT Radii
• Higher harmonic anisotropic flow measurements of charged particles in Pb-Pb collisions at 2.76 TeV
• Measurement of the azimuthal anisotropy for charged particle production in sqrt(s_NN) = 2.76 TeV lead-lead collisions with the ATLAS detector
• Alternative ansatz to wounded nucleon and binary collision scaling in high-energy nuclear collisions
• Triangularity and Dipole Asymmetry in Heavy Ion Collisions
• Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions
• Generic framework for anisotropic flow analyses with multi-particle azimuthal correlations
• Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics
• Measurement of event-plane correlations in sqrt(s_NN)=2.76 TeV lead-lead collisions with the ATLAS detector
• Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV
• Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at a nucleon-nucleon center-of-mass energy of 2.76 TeV
• Momentum spectra, anisotropic flow, and ideal fluids
• Determining initial-state fluctuations from flow measurements in heavy-ion collisions
• Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at sqrt(s[NN]) = 2.76 TeV
• $v_4$, $v_5$, $v_6$, $v_7$: nonlinear hydrodynamic response versus LHC data
• Collective flow in 2.76 A TeV and 5.02 A TeV Pb+Pb collisions
• Extracting the shear viscosity of the quark-gluon plasma from flow in ultra-central heavy-ion collisions
• Characterizing flow fluctuations with moments
• Linear and non-linear flow mode in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 2.76 TeV
• Mode-coupling effects in anisotropic flow in heavy-ion collisions
• Event-plane correlators
• Symmetric cumulants and event-plane correlations in Pb+Pb collisions
• Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Hexagonal flow v_6 as a superposition of elliptic v_2 and triangular v_3 flows
• Hydrodynamic flow amplitude correlations in event-by-event fluctuating heavy-ion collisions
• Differential flow correlations in relativistic heavy-ion collisions

Cited by in corpus (9)

• Longitudinal fluctuations and decorrelations of anisotropic flows at the LHC and RHIC energies
• Higher order Symmetric Cumulants
• Overview of high-density QCD studies with the CMS experiment at the LHC
• Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in PbPb collisions at $\sqrt{s_{\mathrm{NN}}}=$ 2.76 and 5.02 TeV
• Precision tests of the nonlinear mode coupling of anisotropic flow via high-energy collisions of isobars
• Scaling behavior of anisotropic flow harmonics in the far from equilibrium regime
• On differences between even and odd anisotropic-flow harmonics in non-equilibrated systems
• Influence of collective nuclear vibrations on initial state eccentricities in Pb+Pb collisions
• Nonlinear coupling of flow harmonics in heavy-ion collisions