Eur. Phys. J. A (2020) 56: 222
https://doi.org/10.1140/epja/s10050-020-00235-4

Regular Article - Theoretical Physics

On nonlinearity in hydrodynamic response to the initial geometry in relativistic heavy-ion collisions

¹ School of Physical Science and Technology, Yangzhou University, Yangzhou, 225002, Jiangsu, China
² Faculdade de Engenharia de Guaratinguetá, Universidade Estadual Paulista, Guaratinguetá, SP, 12516-410, Brazil
³ Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan, 430074, Hubei, China
⁴ Escola de Engenharia de Lorena, Universidade de São Paulo, Lorena, SP, 12602-810, Brazil
⁵ Instituto de Física, Universidade de São Paulo, C.P. 66318, São Paulo, SP, 05315-970, Brazil
⁶ Instituto de Física, Universidade Federal do Rio de Janeiro, C.P. 68528, Rio de Janeiro, RJ, 21945-970, Brazil
⁷ Instituto de Física, Universidade Federal Fluminense, Niterói, RJ, 24210-346, Brazil

^* e-mail: wlqian@usp.br

Received: 28 May 2020
Accepted: 24 August 2020
Published online: 3 September 2020

Abstract

In the context of event-by-event hydrodynamic description, we analyze the implications of two models characterized by distinct initial conditions. The initial energy density of the first model adopts a Gaussian-type distribution, while those of the second one are features by high energy peripheral tubes. We calibrate the initial conditions of both models so that their initial probability distribution of eccentricity are mostly identical. Subsequently, the resultant scaled probability distributions of collective flow and the correlations between flow harmonic and eccentricity coefficients are investigated. Besides, the calculations are carried out for particle correlations regarding the symmetric cumulant, mixed harmonics, and nonlinear response coefficients. Although the resultant two-particle correlations possess similar shapes, numerical calculations indicate a subtle difference between the two models. To be specific, the difference resides in more detailed observables such as the probability distributions of elliptic flow as well as Pearson correlation coefficient regarding higher-order harmonics. We discuss several essential aspects concerning the linearity and nonlinearity between initial eccentricities and final state anisotropies. Further implications are addressed.