# Correlated event-by-event fluctuations of flow harmonics in Pb-Pb collisions at $\sqrt{s_{_{\rm NN}}}=2.76$ TeV

We report the measurements of correlations between event-by-event fluctuations of amplitudes of anisotropic flow harmonics in nucleus-nucleus collisions, obtained for the first time using a new analysis method based on multiparticle cumulants in mixed harmonics. This novel method is robust against systematic biases originating from non-flow effects and by construction any dependence on symmetry planes is eliminated. We demonstrate that correlations of flow harmonics exhibit a better sensitivity to medium properties than the individual flow harmonics. The new measurements are performed in Pb-Pb collisions at the centre-of-mass energy per nucleon pair of $\sqrt{s_{_{\rm NN}}}=2.76$ TeV by the ALICE experiment at the Large Hadron Collider (LHC). The centrality dependence of correlation between event-by-event fluctuations of the elliptic, $v_2$, and quadrangular, $v_4$, flow harmonics, as well as of anti-correlation between $v_2$ and triangular, $v_3$, flow harmonics are presented. The results cover two different regimes of the initial state configurations: geometry-dominated (in mid-central collisions) and fluctuation-dominated (in the most central collisions). Comparisons are made to predictions from MC-Glauber, viscous hydrodynamics, AMPT and HIJING models. Together with the existing measurements of individual flow harmonics the presented results provide further constraints on initial conditions and the transport properties of the system produced in heavy-ion collisions.

Figures

## Figure 1

 Centrality dependence of observables SC$(4,2)$ (red filled squares) and SC$(3,2)$ (blue filled circles) in Pb-Pb collisions at 2.76 TeV. Systematical errors are represented with boxes. Results for HIJING model are shown with hollow markers.

## Figure 2

 AMPT model predictions are shown as hollow symbols in the (top) and (middle) panels. (top) Comparison of observables SC(4,2) (red filled squares) and SC(3,2) (blue filled circles) to theoretical model from. Solid lines indicate the predictions with constant $\eta/s$, while the dashed lines indicate predictions for different parameterizations of $\eta/s$ temperature dependence (labeled in the same way as in Fig.1 in). (middle) Results divided by $\left< v_m^2\right>\left< v_n^2\right>$. (bottom) Comparison to MC-Glauber using wounded nucleon (WN) and binary collisions (BC) weights.

## Figure 3

 Correlated and anti-correlated event-by-event fluctuations in coordinate (MC-Glauber) and momentum space (data). On the bottom panel we present the normalized SC observables, where pseudorapidity gap $|\Delta\eta| > 1.0$ was applied in both two-particle correlations in denominator used to estimate individual flow harmonics.