Advances in High Energy Physics

Volume 2016 (2016), Article ID 9365637, 13 pages

http://dx.doi.org/10.1155/2016/9365637

## Review of Anisotropic Flow Correlations in Ultrarelativistic Heavy-Ion Collisions

Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, 2100 Copenhagen, Denmark

Received 27 May 2016; Accepted 14 July 2016

Academic Editor: Md. Nasim

Copyright © 2016 You Zhou. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP^{3}.

#### Abstract

Anisotropic flow phenomena are a key probe of the existence of Quark-Gluon Plasma. Several new observables associated with correlations between anisotropic flow harmonics are developed, which are expected to be sensitive to the initial fluctuations and transport properties of the created matter in heavy-ion collisions. I review recent developments of correlations of anisotropic flow harmonics. The experimental measurements, together with the comparisons to theoretical model calculations, open up new opportunities of exploring novel QCD dynamics in heavy-ion collisions.

#### 1. Introduction

One of the fundamental questions in the phenomenology of Quantum Chromo Dynamics (QCD) is, what are the properties of matter at extreme densities and temperatures where quarks and gluons are in a new state of matter, the so-called Quark-Gluon Plasma (QGP)? [1, 2]. Collisions of high-energy heavy ions, at the Brookhaven Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), allow us to create and study the properties of the QGP matter in the laboratory. This matter expands under large pressure gradients, which transfer the inhomogeneous initial conditions into azimuthal anisotropy of produced particles in momentum space. This anisotropy of produced particles is one of the probes of the properties of the QGP [3, 4]. It can be characterized by an expansion of the single-particle azimuthal distribution :where is the azimuthal angle of emitted particles, is the th order flow vector defined as , its magnitude is the th order anisotropic flow harmonic, and its orientation is symmetry plane (participant plane) angle . Alternatively, this anisotropy can be generally given by the joint probability density function (PDF) in terms of and as In the last decade, the experimental measurements of anisotropic flow [5–55], combined with theoretical advances from calculations made in a variety of frameworks [56–62], have led to broad and deep knowledge of initial conditions and properties of the created hot/dense QCD matter. In particular, the precision anisotropic flow measurements based on the huge data collected at the LHC experiments and the successful description from hydrodynamic calculations demonstrate that the QGP created in heavy-ion collisions behaves like a strongly coupled liquid with a very small specific shear viscosity [63–68], which is close to a quantum limit 1/4 [69].

It has been investigated into great details of event-by-event fluctuations of single flow harmonic. Based on the measurements of higher-order cumulants of anisotropic flow [43, 48, 51, 74, 75] and the event-by-event distributions [40], it was realized that the newly proposed Elliptic-Power function [76–78] gives the best description of underlying PDF of single harmonic distributions [72, 79, 80]. On the other hand, it has been known for a while that both the flow harmonic (magnitude) and its symmetry plane (orientation) of the flow vector fluctuate event-by-event [81–83], but only recently and dependent flow angle () and magnitude () were predicted by hydrodynamic calculations [84, 85]. Many indications were quickly obtained in experiments by looking at the deviations from unity of [86] and factorization ratio [52, 55, 86]. These measurements were nicely predicted or reproduced by hydrodynamic calculations and are found to be sensitive to the initial state density fluctuations and/or the shear viscosity of the expanding fireball medium [84, 85, 87]. Most of these above-mentioned studies are focused on the fluctuations of single flow harmonics and their corresponding symmetry planes, as a function of collisions centrality, transverse momentum , and pseudorapidity . Results of correlations between symmetry planes [28, 41] reveal a new type of correlations between different order flow vectors, which was investigated in the observable of before [88–90]. In particular, some of the symmetry planes correlations show quite different centrality dependence from the initial state and final state, and this characteristic sign change during system evolution is correctly reproduced by theoretical calculations [62, 82, 91], thus confirming the validity of hydrodynamic framework in heavy-ion collisions and further yielding valuable additional insights into the fluctuating initial conditions and hydrodynamic response [62, 82, 92].

In addition to all these observables, the (anti)correlations between anisotropic flow harmonics and are found to be extremely interesting [45, 62, 70, 71, 93]. A completely new set of information on the joint probability density function (PDF) can be obtained from the rich correlation pattern observed in experiments. On the other hand, no existent theoretical calculations [62, 70, 71, 93] could provide quantitative descriptions of data [36]. Thus, it is crucial to investigate in depth the relationship between different flow harmonics: whether they are correlated, anticorrelated, or not correlated from both experimental and theoretical points of view.

#### 2. Correlations of and Fluctuations

It is found recently that the relationship between different order flow harmonics can be used to probe the initial state conditions and the hydrodynamic response of the QGP [36, 71, 93–95]. In order to better understand the event-by-event distribution, it is critical to investigate the relationship between and . Considering the naive ellipsoidal shape of the overlap region in noncentral heavy-ion collisions generating nonvanishing even flow harmonics , the correlations between the even flow harmonics are expected. However, it is not straightforward to use geometrical argument to explain the relationship between even flow harmonics for central collisions, where all the harmonics are driven by fluctuations instead of geometry, and to explain the relationship between even and odd flow harmonics for central and noncentral collisions [80]. A linear correlation function was proposed to study the relationship between and [83]. It is defined aswhere is the standard deviation of the quantity ; is 1 (or −1) if and are linearly (antilinearly) correlated and is 0 if they are not correlated. It was shown in Figure 1 that there is an anticorrelation between and , while a correlation was observed between and . In addition, it was demonstrated that depends on both the initial conditions and , while is only sensitive to [83]. Nevertheless, it cannot be accessible easily in experimental measurements, which rely on two-particle and multiparticle correlations techniques. Thus, it is critical to find an observable which studies the relationship between flow harmonics without contributions from symmetry plane correlations and can be accessed with observable techniques from experiments. Two different approaches, named and , are discussed in the following section.