**Lock**

Correlations between moments of different flow coefficients are measured in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 5.02$ TeV recorded with the ALICE detector. These new measurements are based on multiparticle mixed harmonic cumulants calculated using charged particles in the pseudorapidity region $|\eta|<~0.8$ with the transverse momentum range $0.2 <~ p_{\rm T} <~ 5.0$ GeV/$c$. The centrality dependence of correlations between two flow coefficients as well as the correlations between three flow coefficients, both in terms of their second moments, are shown. In addition, a collection of mixed harmonic cumulants involving higher moments of $v_2$ and $v_3$ is measured for the first time, where the characteristic signature of negative, positive and negative signs of four-, six- and eight-particle cumulants are observed, respectively. The measurements are compared to the hydrodynamic calculations using iEBE-VISHNU with AMPT and TRENTo initial conditions. It is shown that the measurements carried out using the LHC Run 2 data in 2015 have the precision to explore the details of initial-state fluctuations and probe the nonlinear hydrodynamic response of $v_2$ and $v_3$ to their corresponding initial anisotropy coefficients $\varepsilon_2$ and $\varepsilon_3$. These new studies on correlations between three flow coefficients as well as correlations between higher moments of two different flow coefficients will pave the way to tighten constraints on initial-state models and help to extract precise information on the dynamic evolution of the hot and dense matter created in heavy-ion collisions at the LHC.

Submitted to: **PLB **

e-Print: arXiv:2102.12180 | PDF | inSPIRE