First measurement of symmetric cumulants of hexagonal flow harmonics in Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5.02 TeV

TL;DR

This study reports the first measurement of symmetric cumulants involving flow harmonics up to the hexagonal order in Pb--Pb collisions at $\sqrt{s_{\rm NN}}=5.02$ TeV with the ALICE detector, defining and measuring NSC$(m,n)$ to quantify event-by-event correlations among $v_n$ up to $v_6$. The analysis includes detailed event/track selection and systematic uncertainty assessments, and compares the data to EKRT+hydrodynamics and TRENTo+iEBE-VISHNU models, highlighting the sensitivity of higher-order observables to initial conditions and transport properties. The results reveal nontrivial centrality dependencies and sign patterns, with higher-order NSC generally challenging current models, thereby providing independent constraints for Bayesian parameter estimation of QGP properties such as $\eta/s(T)$. Overall, NSC observables prove valuable for disentangling initial-state effects from nonlinear hydrodynamic response and for refining theoretical descriptions of the QGP in heavy-ion collisions.

Abstract

Correlations between event-by-event fluctuations of anisotropic flow harmonics are measured in Pb$-$Pb collisions at a center-of-mass energy per nucleon pair of 5.02 TeV, as recorded by the ALICE detector at the LHC. This study presents correlations up to the hexagonal flow harmonic, $v_6$, which was measured for the first time. The magnitudes of these higher-order correlations are found to vary as a function of collision centrality and harmonic order. These measurements are compared to viscous hydrodynamic model calculations with EKRT initial conditions and to the iEBE-VISHNU model with TRENTo initial conditions. The observed discrepancies between the data and the model calculations vary depending on the harmonic combinations. Due to the sensitivity of model parameters estimated with Bayesian analyses to these higher-order observables, the results presented in this work provide new and independent constraints on the initial conditions and transport properties in theoretical models used to describe the system created in heavy-ion collisions.

Figures (3)

• Figure 1: Sensitivity of the model parameters in Bayesian analysis to the flow observables, shown as a color map. Light yellow shades represent low or no sensitivity, whereas orange and red colors represent moderate or strong sensitivities to the corresponding model parameter variation, respectively. The sensitivity analysis is based on the TRENTo+iEBE-VISHNU model Moreland:2014oya. Several key parameters are displayed, including $\eta/s(T)$, $\zeta/s(T)$, $\tau_{\rm fs}$, and $T_{\rm switch}$. More details can be found in Ref. Parkkila:2021yha.
• Figure 2: The centrality dependence of the NSC observables. The previously published lower-order harmonics ALICE:2021adw are marked with asterisk (*). The statistical and total systematic uncertainties are shown with vertical lines and boxes, respectively.
• Figure 3: The centrality dependence of NSC($m$,$n$) in $\hbox{Pb--Pb}\xspace$ collisions at $\sqrt{s_{\mathrm{NN}}}\xspace=5.02$ TeV. Results for each observable are compared with the final-state predictions from the event-by-event EKRT + viscous hydrodynamic calculations Niemi:2015qia and TRENTo+iEBE-VISHNU MAP (2022), as well as with the initial-state calculations from EKRT and TRENTo. Panels (a) to (c) present data from Ref. ALICE:2021adw. The statistical and total systematic uncertainties of the data are shown with vertical lines and boxes, respectively. The model results are shown as colored bands with the width of the band denoting the statistical uncertainties.