Advances in High Energy Physics

Volume 2016, Article ID 2836989, 16 pages

http://dx.doi.org/10.1155/2016/2836989

## The First Moment of Azimuthal Anisotropy in Nuclear Collisions from AGS to LHC Energies

Department of Physics, Kent State University, Ohio 44242, USA

Received 22 June 2016; Accepted 29 September 2016

Academic Editor: Emil Bjerrum-Bohr

Copyright © 2016 Subhash Singha et al. 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

We review topics related to the first moment of azimuthal anisotropy (), commonly known as directed flow, focusing on both charged particles and identified particles from heavy-ion collisions. Beam energies from the highest available, at the CERN LHC, down to projectile kinetic energies per nucleon of a few GeV per nucleon, as studied in experiments at the Brookhaven AGS, fall within our scope. We focus on experimental measurements and on theoretical work where direct comparisons with experiment have been emphasized. The physics addressed or potentially addressed by this review topic includes the study of Quark Gluon Plasma and, more generally, investigation of the Quantum Chromodynamics phase diagram and the equation of state describing the accessible phases.

#### 1. Introduction

The purpose of relativistic nuclear collision experiments is the creation and study of nuclear matter at high energy densities. Experiments have established a new form of strongly interacting matter, called Quark Gluon Plasma (QGP) [1–7]. Collective motion of the particles emitted from such collisions is of special interest because it is sensitive to the equation of state in the early stages of the reaction [8–10]. Directed flow was the first type of collective motion identified among the fragments from nuclear collisions [11–13] and, in current analyses, is characterized by the first harmonic coefficient in the Fourier expansion of the azimuthal distribution of the emitted particles with respect to each event’s reaction plane azimuth () [14–16]:where is the azimuth of a charged particle, or more often, the azimuth of a particular particle species, and the angle brackets denote averaging over all such particles in all events. In some experimental analyses, is evaluated directly from (1); then a correction is applied for reaction plane resolution [15], whereas, in a typical modern analysis method, the directed flow correlation is extracted using cumulants [16]. In general, is of interest when plotted as a function of rapidity, , or sometimes pseudorapidity , where is the polar angle of the particle. The dependence of on collision centrality and on transverse momentum, , can offer additional insights.

Until relatively recently [17, 18], the rapidity-even component was always assumed to be zero or negligible in mass-symmetric collisions. In fact, fluctuations within the initial-state colliding nuclei, unrelated to the reaction plane, can generate a significant signal [17, 18]. This fluctuation effect falls beyond the scope of the present review, which focuses on fluid-like directed flow, , as per (1), and from here on, for mass-symmetric collisions implicitly signifies .

During the first decade of the study of in nuclear collisions, it was more commonly called sideward flow. It refers to a sideward collective motion of the emitted particles and is a repulsive collective deflection in the reaction plane. By convention, the positive direction of is taken to be the direction of “bounce-off” of projectile spectators in a fixed target experiment [8, 10]. Models imply that directed flow, especially the component closest to beam rapidity, is initiated during the passage time of the two colliding nuclei; the typical time-scale for this is [9, 10], where and are the nuclear radius and Lorentz factor, respectively. This is even earlier than the still-early time when elliptic flow, , is mostly imparted. Thus can probe the very early stages of the collision [19, 20], when the deconfined state of quarks and gluons is expected to dominate the collision dynamics [9, 10]. Both hydrodynamic [21, 22] and transport model [23, 24] calculations indicate that the directed flow of charged particles, especially baryons at midrapidity, is sensitive to the equation of state and can be used to explore the QCD phase diagram.

The theoretical work leading to the prediction of collective flow in nuclear collisions evolved gradually. In the mid-1950s, Belenkij and Landau [25] were the first to consider a hydrodynamic description of nuclear collisions. During the 1970s, as the Bevatron at Lawrence Berkeley National Lab was converted for use as the first accelerator of relativistic nuclear beams, the idea of hydrodynamic shock compression of nuclear matter emerged [26–28], and these developments in turn led to increasingly realistic predictions [11, 12, 29] that paved the way for the first unambiguous measurement of directed flow at the Bevalac in the mid-1980s [13]. A frequent focus of theory papers during the subsequent years was the effort to use directed flow measurements to infer the incompressibility of the nuclear equation of state in the hadron gas phase and to infer properties of the relevant momentum-dependent potential [8, 10]. The observed directed flow at AGS energies [30–38] and below is close to a linear function of rapidity throughout the populated region, and the slope can adequately quantify the strength of the signal. At SPS energies and above [39–47], a more complex structure is observed in , with the slope in the midrapidity region being different from the slope in the regions closer to beam rapidity.

Various models also exhibit this kind of behavior. At these energies, both hydrodynamic and nuclear transport calculations predict a negative sign for charged particle near midrapidity, where pions are the dominant particle species. This negative near midrapidity has been given various names in the literature: “third flow component” [48], “antiflow” [49], or “wiggle” [10, 22, 50]. This phenomenon has been discussed as a possible QGP signature, and a negative for baryons has been argued [22] to be particularly significant. However, some aspects of antiflow can be explained in a model with only hadronic physics [50, 51] by assuming either incomplete baryon stopping with a positive space-momentum correlation [50], or full stopping with a tilted source [52].

A three-fluid hydrodynamic model [22] predicts a monotonic trend in net-baryon directed flow versus beam energy in the case of a purely hadronic equation of state, whereas a prominent minimum at AGS energies, dubbed the “softest point collapse,” is predicted when the equation of state incorporates a first-order phase transition between hadronic and quark-gluonic matter. Recent measurements of both proton and net-proton directed flow at RHIC [47] indeed indicate nonmonotonic directed flow as a function of beam energy, with the minimum lying between 11.5 and 19.6 GeV in . However, more recent hydrodynamic and nuclear transport calculations which incorporate significant theoretical improvements (see Section 5) do not reproduce the notable qualitative features of the data and therefore cast doubt on any overall conclusion about the inferred properties of the QCD phase diagram. Directed flow has also been measured at the LHC [53]. A negative slope of is observed for charged particles, but its magnitude is much smaller than at RHIC, which is thought to be a consequence of the smaller tilt of the participant zone at the LHC.

In this article, we review a representative set of directed flow results spanning AGS to LHC energies. In Sections 2 and 3, we discuss measurements of for charged particles in mass-symmetric and mass-asymmetric collisions, respectively. In Section 4, we cover measurements of for various identified particle species. Section 5 reviews some recent model calculations which lend themselves to direct comparisons with directed flow data. Section 6 presents a summary and future outlook.

#### 2. Differential Measurements of Charged Particle Directed Flow

In this section, we review measurements of for all charged particles in cases where individual species were not identified. Studies of the dependence on transverse momentum , pseudorapidity , beam energy , system size, and centrality are included.

##### 2.1. Dependence of on Transverse Momentum

The -dependence of for charged particles has been studied by the STAR experiment at RHIC [43, 44]. Figure 1(a) presents directed flow results for Au+Au collisions in two centrality intervals, 5–40% and 40–80%, and in two regions of pseudorapidity, and . In this case, because of the odd-functional property of , the backward pseudorapidity region by convention has its sign of reversed before summing over the indicated gate in pseudorapidity. These measurements represent the first instance of using only spectators to determine the estimated azimuth of the reaction plane [54–56].