Advances in High Energy Physics

Volume 2017 (2017), Article ID 1248563, 15 pages

https://doi.org/10.1155/2017/1248563

## A Review of Elliptic Flow of Light Nuclei in Heavy-Ion Collisions at RHIC and LHC Energies

^{1}Utrecht University, P.O. Box 80000, 3508 TA Utrecht, Netherlands^{2}School of Physical Sciences, National Institute of Science Education and Research, Jatni 752050, India^{3}Indian Institute of Science Education and Research, Tirupati 517507, India

Correspondence should be addressed to Md. Rihan Haque

Received 30 June 2016; Revised 27 September 2016; Accepted 29 May 2017; Published 15 August 2017

Academic Editor: Shi-Hai Dong

Copyright © 2017 Md. Rihan Haque 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 present a review of the measurements of elliptic flow () of light nuclei (, , , , and ) from the RHIC and LHC experiments. Light (anti)nuclei have been compared with that of (anti)proton. We observed a similar trend in light nuclei to that in identified hadron with respect to the general observations such as dependence, low mass ordering, and centrality dependence. We also compared the difference of nuclei and antinuclei with the corresponding difference of of proton and antiproton at various collision energies. Qualitatively they depict similar behavior. We also compare the data on light nuclei to various theoretical models such as blast-wave and coalescence. We then present a prediction of for and using coalescence and blast-wave models.

#### 1. Introduction

The main goals of high energy heavy-ion collision experiments have primarily been to study the properties of Quark Gluon Plasma (QGP) and the other phase structures in the QCD phase diagram [1–11]. The energy densities created in these high energy collisions are similar to that found in the universe, microseconds after the Big Bang [5–8, 12–14]. Subsequently, the universe cooled down to form nuclei. It is expected that high energy heavy-ion collisions will allow studying the production of light nuclei such as , , , and their corresponding antinuclei. There are two possible production mechanisms for light (anti)nuclei. The first mechanism is thermal production of nucleus-antinucleus pairs in elementary nucleon-nucleon or parton-parton interactions [15–21]. However, due to their small (~few MeV) binding energies, the directly produced nuclei or antinuclei are likely to break up in the medium before escaping. The second mechanism is via final state coalescence of produced (anti)nucleons or from transported nucleons [22–36]. The quark coalescence as a mechanism of hadron production at intermediate transverse momentum has been well established by studying the number of constituent quarks (NCQ) scaling for of identified hadrons measured at RHIC [37–45]. Light nuclei may also be produced via coalescence of quarks similar to the hadrons. But the nuclei formed via quark coalescence are highly unlikely to survive in the high temperature environment due to their small binding energies. In case of hadron formation by quark coalescence, the momentum space distribution of quarks is not directly measurable in experiments. However, in case of nucleon coalescence, momentum space distributions of both the constituents (nucleons) and the products (nuclei) are measurable in heavy-ion collision experiments. Therefore, measurements of of light nuclei provide a tool to understand the production mechanism of light nuclei and freeze-out properties at a later stage of the evolution. It also provides an excellent opportunity to understand the mechanism of coalescence at work in high energy heavy-ion collisions.

The production of light (anti)nuclei has been studied extensively at lower energies in Bevelac at LBNL [24, 46–49], AGS at RHIC [50–53], and SPS at CERN [54–58]. In the AGS experiments, it was found that the coalescence parameter () is of similar magnitude for both and indicating similar freeze-out hypersurface of nucleons and antinucleons. Furthermore, the dependence of on collision energy and indicated that light nuclei production is strongly influenced by the source volume and transverse expansion profile of the system [58, 59]. In this paper, we review the results of elliptic flow of light nuclei measured at RHIC and LHC and discuss the possible mechanisms for the light nuclei production.

The paper is organized as follows. Section 2 briefly describes the definition of , identification of light (anti)nuclei in the experiments and measurement of of light (anti)nuclei. In Section 3, we present the results for minimum bias collisions from various experiments. We also discuss the centrality dependence, difference between nuclei and antinuclei , and the energy dependence of deuteron . In the same section, we present the atomic mass number scaling and also compare the experimental results with various theoretical models. Finally in Section 4, we summarize our observations and discuss the main conclusions of this review.

#### 2. Experimental Method

##### 2.1. Elliptic Flow

The azimuthal distribution of produced particles in heavy-ion collision can be expressed in terms of a Fourier series,where is the azimuthal angle of produced particle, is called the reaction plane angle, and the Fourier coefficients , , and so on are called flow coefficients [60]. is defined as the angle between the impact parameter vector and the -axis of the reference detector in the laboratory frame. Since it is impossible to measure the direction of impact parameter in heavy-ion collisions, a proxy of , namely, the event plane angle , is used for the flow analysis in heavy-ion collisions [61]. is measured with respect to the 2nd-order event plane angle [61]. is calculated using the azimuthal distribution of the produced particles. In an event with particles, the event plane angle is defined as [61] and are defined aswhere are weights given to each particle to optimise the event plane resolution [61, 62]. Usually the magnitude of particle transverse momentum is used as weights as increases with . Special techniques are followed while calculating the event plane angle so that it does not contain the particle of interest whose is to be calculated (self-correlation) and also the nonflow effects (e.g., jets and short range correlations) are removed as much as possible [41, 42, 61, 63]. Heavy-ion experiments use the -subevent plane method to calculate the elliptic flow of identified hadrons as well as for light nuclei. In this method, each event is divided into two subevents in two different -windows (e.g., positive and negative ). Then two subevent plane angles are calculated with the particles in each subevent. Each particle with a particular is then correlated with the subevent plane of the opposite . This ensures that the particle of interest is not included in the calculation of event plane angle. A finite gap is applied between the two subevents to reduce short range correlations which does not originate from flow.

The distribution of the event plane angles should be isotropic in the laboratory frame for a azimuthally isotropic detector. If the distribution of the event plane angles is not flat in the laboratory frame (due to detector acceptance and/or detector inefficiency) then special techniques are applied to make the distribution uniform. The popular methods to make the distribution uniform is the -weight and recentering [64, 65]. In the -weight method, one takes the actual azimuthal distribution of the produced particle, averaged over large sample of events, and then uses inverse of this distribution as weights while calculating the correlation of the particles with the event plane angle [64, 65]. In the recentering method, one subtracts and from the event-by-event and , respectively, where and denote the average of and over a large sample of similar events. The main disadvantage of applying one of these methods is that it does not remove the contribution from higher flow harmonics. Therefore, another correction method known as the shift correction is used to remove the effects coming from higher flow harmonics. In this method, one fits the distribution (after applying -weight and/or recentering method) averaged over all events, with a Fourier function. The Fourier coefficients from this fit (obtained as fit parameters) are used to shift of each event, to make the distribution uniform in the laboratory frame [64, 65].

Since the number of particles produced in heavy-ion collisions are finite, the calculated event plane angle may not coincide with . For this reason, the measured with respect to is corrected with the event plane resolution factor , where

In order to calculate the event plane resolution, one calculates two subevent plane angles and , where and correspond to two independent subevents. If the multiplicities of each subevent are approximately half of the full event plane, then the resolution of each of subevent plane can be calculated as [60, 61],However, the full event plane resolution can be expressed aswhere = and , are modified Bessel functions [60, 61]. The parameter is inversely proportional to the square-root of , the number of particles used to determine the event plane [60, 61]. To calculate the resolution for full event plane (), one has to solve (6) iteratively for the value of using the subevent plane resolution () which is calculated experimentally using (5). The value is then multiplied with as is proportional to and reused in (6) to calculate the resolution of the full event plane. In a case of very low magnitudes, the full event plane resolution can be approximately given as [60, 61]The procedure for calculating full and subevent plane resolutions using subevent plane angles and various approximations is discussed in detail in [60, 61].

##### 2.2. Data on Light Nuclei

For this review, we have collected light nuclei data from the STAR [63] and PHENIX [66] experiments at RHIC and ALICE experiment at LHC [67]. Table 1 summarizes the measurement of light nuclei available till date.