Abstract
The Fourier analysis of the final particle distribution followed by cumulant study of the Fourier coefficient event-by-event fluctuation is one of the main approaches for testing the collective evolution in the heavy-ion collision. Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them. In particular, we show that there are 33 distinct cumulants with order 2, 3, 4, 5 and harmonics 2, 3, 4, 5. We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on T_mathtt{R}ENTo+VISH2+1+UrQMD. We compare the simulation with those normalized cumulants that the LHC has measured and predict the unmeasured ones. Comparing the initial and final state fluctuation normalized cumulants, we compute the linear and nonlinear hydrodynamic response couplings. We finally introduce the genuine three-particle correlation function containing information of all third-order cumulants.
Highlights
Using a multidimensional generating function, we propose a method to extract any possible cumulant of multiharmonic flow fluctuations and classify them in terms of the order of cumulants and harmonics involved in them
We compute the normalized version of these cumulants from hydrodynamic simulation for Pb–Pb collisions based on TRENTo+VISH2+1+UrQMD
The imprints of different stages of a heavy-ion collision, preequilibrium, initial state, collective evolution, and freezeout are cumulatively encoded in the flow harmonics
Summary
The anisotropic particle emission in the azimuthal direction [11,12,13] is one of the most important evidences of collectivity in ultrarelativistic heavy-ion collisions. The package returns the cumulants in three different forms: in terms of vn and ψn moment, final particle azimuthal angle correlations, and Q-vectors (see Eq (29)) notations. For the case involving simultaneous harmonics n = 2, 4, 5, cumulants starts from fifth order with two different forms (see Table 1). We study the flow-induced 3PC for harmonics 2 to 5 via our hydrodynamic simulation This quantity contains information on all third-order cumulants. A realistic Monte Carlo study of the first Fourier-cumulant expansion terms is presented in Sect. 4. The linear and nonlinear hydrodynamic response couplings are extracted by comparing the initial state, and final state fluctuation normalized cumulants in Sect. 5. we study genuine three-particle correlation functions in Sect. In Appendix B, a technical study about the statistical fluctuation of multiharmonic correlations is presented. Detail of some derivations in the text is presented in the Appendices C and D
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