Higher order Symmetric Cumulants

Abstract

We present the generalization of recently introduced observables for the studies of correlated fluctuations of different anisotropic flow amplitudes, dubbed Symmetric Cumulants. We introduce a new set of higher order observables and outline a unique way how the genuine multi-harmonic correlations can be extracted from multi-particle azimuthal correlators. We argue that correlations among flow amplitudes can be studied reliably with the general mathematical formalism of cumulants only if that formalism is applied directly on the flow amplitudes. We have tested all the desired properties of new observables with the carefully designed Toy Monte Carlo studies. By using the realistic iEBE-VISHNU model, we have demonstrated that their measurements are feasible and we have provided the predictions for the centrality dependence in Pb--Pb collisions at LHC energies. A separate study was performed for their values in the coordinate space. The new observables contain information which is inaccessible to individual flow amplitudes and correlated fluctuations of only two flow amplitudes, and therefore they provide further and independent constraints for the initial conditions and the properties of Quark-Gluon Plasma in high-energy nuclear collisions.

arXiv comment30 pages, 12 figures. Major revision. This version was accepted for publication in Physical Review C

References in corpus (61)

• Flow Study in Relativistic Nuclear Collisions by Fourier Expansion of Azimuthal Particle Distributions
• HIJING 1.0: A Monte Carlo Program for Parton and Particle Production in High Energy Hadronic and Nuclear Collisions
• Derivation of transient relativistic fluid dynamics from the Boltzmann equation
• Fluctuating Glasma initial conditions and flow in heavy ion collisions
• QCD Equation of State and Hadron Resonance Gas
• Flow analysis with cumulants: direct calculations
• Triangularity and Dipole Asymmetry in Heavy Ion Collisions
• Flow analysis from multiparticle azimuthal correlations
• Properties of hot and dense matter from relativistic heavy ion collisions
• Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions
• New method for measuring azimuthal distributions in nucleus-nucleus collisions
• Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions
• Dissipative relativistic fluid dynamics: a new way to derive the equations of motion from kinetic theory
• 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
• Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions
• Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV
• Determining initial-state fluctuations from flow measurements in heavy-ion collisions
• Ultra-relativistic nuclear collisions: event shape engineering
• Investigations of anisotropic flow using multi-particle azimuthal correlations in pp, p-Pb, Xe-Xe, and Pb-Pb collisions at the LHC
• Evidence of sub-nucleonic degrees of freedom in J/$\psi$ photoproduction in ultraperipheral collisions at the CERN Large Hadron Collider
• Measurement of the correlation between flow harmonics of different order in lead-lead collisions at $\sqrt{s_{NN}}$=2.76 TeV with the ATLAS detector
• Estimating initial state and quark-gluon plasma medium properties using a hybrid model with nucleon substructure calibrated to $p$-Pb and Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
• Revealing long-range multi-particle collectivity in small collision systems via subevent cumulants
• Collective flow in 2.76 A TeV and 5.02 A TeV Pb+Pb collisions
• Effect of the QCD equation of state and strange hadronic resonances on multiparticle correlations in heavy ion collisions
• Characterizing flow fluctuations with moments
• Multiparticle collectivity from initial state correlations in high energy proton-nucleus collisions
• v4: A small, but sensitive observable for heavy ion collisions
• Shrinking the Quark Gluon Plasma
• Observation of correlated azimuthal anisotropy Fourier harmonics in pp and pPb collisions at the LHC
• Plane correlations and hydrodynamic simulations of heavy ion collisions
• Multi-particle and charge-dependent azimuthal correlations in heavy-ion collisions at the Relativistic Heavy-Ion Collider
• Event-shape fluctuations and flow correlations in ultra-relativistic heavy-ion collisions
• Longitudinal Decorrelation of Anisotropic Flows in Heavy-ion Collisions at the CERN Large Hadron Collider
• Parton model description of multiparticle azimuthal correlations in $pA$ collisions
• Correlations of flow harmonics in 2.76A TeV Pb--Pb collisions
• Symmetric cumulants and event-plane correlations in Pb+Pb collisions
• Constraints on rapidity-dependent initial conditions from charged particle pseudorapidity densities and two-particle correlations
• Correlated long-range mixed-harmonic fluctuations measured in $pp$, $p$+Pb and low-multiplicity Pb+Pb collisions with the ATLAS detector
• Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV
• Systematic procedure for analyzing cumulants at any order
• Fluctuations of anisotropic flow in Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV with the ATLAS detector
• Anisotropic distributions in a multi-phase transport model
• Hydrodynamic Predictions for Mixed Harmonic Correlations in 200 GeV Au+Au Collisions
• Glauber Monte Carlo predictions for ultra-relativistic collisions with ${}^{16}\mathrm{O}$
• Longitudinal decorrelation measures of flow magnitude and event-plane angles in ultra-relativistic nuclear collisions
• Hydrodynamic flow amplitude correlations in event-by-event fluctuating heavy-ion collisions
• Study of the sensitivity of observables to hot spot size in heavy ion collisions
• A method for studying the rapidity fluctuation and decorrelation of harmonic flow in heavy-ion collisions
• Multiparticle azimuthal cumulants in p+Pb collisions from a multiphase transport model
• Symmetric cumulants as a probe of the proton substructure at LHC energies
• Differential flow correlations in relativistic heavy-ion collisions
• Systematic study of symmetric cumulants at $\sqrt{s_{NN}}$ = 200 GeV in Au+Au collision using transport approach
• Nonlinear coupling of flow harmonics: Hexagonal flow and beyond
• Non-Bessel-Gaussianity and Flow Harmonic Fine-Splitting
• Primordial non-Gaussianity in heavy-ion collisions
• ALICE measurements of flow coefficients and their correlations in small (pp and p-Pb) and large (Xe-Xe and Pb-Pb) collision systems
• Latest results from the EbyE NLO EKRT model
• Measurements of correlations of anisotropic flow harmonics in Pb--Pb Collisions with ALICE
• Nonlinear coupling of flow harmonics in heavy-ion collisions

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• The ALICE experiment: a journey through QCD
• Theoretical and Experimental Constraints for the Equation of State of Dense and Hot Matter
• New constraints for QCD matter from improved Bayesian parameter estimation in heavy-ion collisions at LHC
• Generic algorithm for multi-particle cumulants of azimuthal correlations in high energy nucleus collisions
• Constraining the nucleon size with relativistic nuclear collisions
• QCD Challenges from pp to A-A Collisions
• Multi-harmonic correlations of different flow amplitudes in Pb-Pb collisions at $\sqrt{s_{{}_{\mathrm{NN}}}}=2.76$ TeV
• Higher order cumulants of transverse momentum and harmonic flow in relativistic heavy ion collisions
• Factorization breaking for higher moments of harmonic flow
• Multivariate cumulants in flow analyses: The Next Generation
• Characterizing the initial and final state effects of relativistic nuclear collisions
• Collectivity in large and small systems formed in ultrarelativistic collisions
• Multi-particle correlations, cumulants, and moments sensitive to fluctuations in rare-probe azimuthal anisotropy in heavy ion collisions
• Utilizing maximum likelihood estimator for flow analysis
• Higher-order correlations between different moments of two flow amplitudes in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}=5.02$ TeV
• Systematic Analysis of Flow Distributions
• Event-by-event cumulants of azimuthal angles
• Higher-order symmetry plane correlations in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Symmetric cumulant $s{c}_{2,4}\left\{4\right\}$ and asymmetric cumulant $a{c}_2\left\{3\right\}$ from transverse momentum conservation and flow
• Probing Nuclear Geometry through Multi-Particle Azimuthal Correlations and Rapidity-Even Dipolar Flow in ${}^{16}$O+${}^{16}$O Collisions
• Measurements of mixed harmonic cumulants in Pb-Pb collisions at $\sqrt{{\text{s}}_{\mathrm{NN}}}=5.02$ TeV
• Measuring differential particle correlations in relativistic nuclear collisions
• First measurement of symmetric cumulants of hexagonal flow harmonics in Pb$-$Pb collisions at $\sqrt{s_{\mathrm{NN}}}$ = 5.02 TeV
• Characterizing the initial state and dynamical evolution in XeXe and PbPb collisions using multiparticle cumulants
• Flow harmonic correlations via multi-particle symmetric and asymmetric cumulants in Au+Au collisions at \(\sqrt{s_{NN}}\) = 200 GeV