Advances in High Energy Physics

Volume 2016 (2016), Article ID 4236492, 9 pages

http://dx.doi.org/10.1155/2016/4236492

## Spectra and Elliptic Flow of (Multi)Strange Hadrons at RHIC and LHC within Viscous Hydrodynamics + Hadron Cascade Hybrid Model

^{1}School of Science, Huzhou University, Huzhou 313000, China^{2}Department of Physics and State Key Laboratory of Nuclear Physics and Technology, Peking University, Beijing 100871, China

Received 8 March 2016; Accepted 14 August 2016

Academic Editor: Shusu Shi

Copyright © 2016 Xiangrong Zhu. 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

Using the ()-dimensional ultrarelativistic viscous hydrodynamics + hadron cascade, VISHNU, hybrid model, we study the -spectra and elliptic flow of , , and in Au + Au collisions at = 200 GeV and in Pb + Pb collisions at = 2.76 TeV. Comparing our model results with the data measurements, we find that the VISHNU model gives good descriptions of the measurements of these strange and multistrange hadrons at several centrality classes at RHIC and LHC. Mass ordering of elliptic flow among , , , , , and are further investigated and discussed at the two collision systems. We find that, at both RHIC and LHC, mass ordering among , , , and is fairly reproduced within the VISHNU hybrid model, and more improvements are needed to be implemented for well describing mass ordering among , , and .

#### 1. Introduction

Ultrarelativistic heavy-ion collisions at the BNL Relativistic Heavy-Ion Collider (RHIC) and CERN Large Hadron Collider (LHC) are used to produce and study a hot and dense medium consisting of strongly interacting quarks and gluons, namely, Quark-Gluon Plasma (QGP), which is expected to exist in the early stage of the universe, and to understand its properties, such as the equation of state (EoS) and transport coefficients. The hadronic interactions are expected to have less influence on the multistrange hadrons, such as and , due to their much smaller hadronic cross-sections. Therefore, final observables of these multistrange hadrons are more sensitive to the early (partonic) stage of the collision. In the past few decades, different aspects of strange and multistrange hadrons have been investigated theoretically [1–13] and experimentally [14–24].

Anisotropic flow, which is considered as an evidence for the QGP formation, typically displays the collective behavior of the final emitted particles. It can be characterized by the coefficients of the Fourier expansion of the final particle azimuthal distribution defined as [25]where is th order anisotropic flow harmonic with its corresponding reaction plane angle and is the azimuthal angle of the final emitted particles. Recently, the anisotropic flow and other soft hadron data of all charged and identified hadrons at the RHIC and LHC have been studied by many groups within the framework of hydrodynamics [13, 26–36]. VISHNU is a hybrid model [37] for single-shot simulations of heavy-ion collisions, which connects the ()-dimensional viscous hydrodynamics with a hadronic afterburner. Employing the VISHNU hybrid model, the specific QGP shear viscosity values of are extracted from the elliptic flow measurements of charged hadrons with MC-KLN initial conditions [29]. With the extracted , the VISHNU provides good descriptions of the soft hadron data of , , and at the RHIC and LHC [30]. Compared with other hadrons, anisotropy flow of (multi)strange particles is mainly produced in the QGP stage and less contaminated by the subsequent hadronic interactions. Meanwhile, the -spectra and elliptic flow for , , and have been measured in the Au + Au collisions at the RHIC [17–20] and Pb + Pb collisions at the LHC [21–23]. Therefore, it is timely to systematically study these strange and multistrange hadrons at RHIC and LHC via the VISHNU hybrid model.

In this paper, we investigate the -spectra and elliptic flow for (multi)strange hadrons in Au + Au collisions at = 200 GeV and in Pb + Pb collisions at = 2.76 TeV within the viscous hydrodynamic hybrid model VISHNU. The paper is organized as follows. Section 2 briefly introduces the VISHNU hybrid model and its setup in the calculations. Section 3 compares our VISHNU results in Au + Au collisions and Pb + Pb collisions with the measurements from the STAR at RHIC and ALICE at LHC, respectively, mainly including -spectra and differential elliptic flow for , , and . In Section 4, the mass ordering of elliptic flow among , , , , , and is studied and discussed at the RHIC and LHC energies. Finally, we summarize our works and give a brief outlook for the future in Section 5.

#### 2. Setup of the Calculation

We here give brief descriptions of the inputs and setup of VISHNU calculations for the soft data at the RHIC and LHC energies. The VISHNU [37] hybrid model consists of two parts, which are the ()-dimensional ultrarelativistic viscous hydrodynamics VISH2+1 [39, 40] for the expansion of strongly interacting matter QGP and a microscopic hadronic cascade model (UrQMD) [41, 42] for the hadronic evolution. In the calculations a switching temperature of 165 MeV is set for the transition from the macroscopic to microscopic approaches in VISHNU. This switching temperature value is close to the QCD phase transition temperature [43–46]. We input the equation of state (EoS) s95p-PCE [47, 48] for the hydrodynamic evolution above the switching temperature . The s95p-PCE, which accounts for the chemical freeze-out at = 165 MeV, was constructed by combing the lattice QCD data at high temperature with a chemically frozen hadron resonance gas at low temperature.

Following [29, 30], we input MC-KLN initial conditions [49–51] and start the hydrodynamic simulations at . For improving computational efficiency, we implement single-shot simulations [13, 29, 30, 37, 38, 52] with smooth initial entropy density profiles generated by the MC-KLN model. The smooth initial entropy densities are obtained by averaging over a large number of fluctuating entropy density profiles within a specific centrality class. The initial density profiles are initialized with the reaction plane method, which was once used in [29, 30, 38]. Considering the conversion from total initial entropies to final multiplicity of all charged hadrons, we do the centrality selection through the distribution of total initial entropies that are obtained from the event-by-event fluctuating profiles. Such centrality classification was firstly used by Shen et al. in [53], which is more close to the experimental one defined from the measured multiplicity distributions. The normalization factors for the initial entropy densities in Au + Au collisions and Pb + Pb collisions are, respectively, fixed to reproduce the charged hadron multiplicity density with at the RHIC [54] and at the LHC [55] at most central collisions. The parameter in the MC-KLN model, which quantifies the gluon saturation scale in the initial gluon distributions [50], is tuned to at the RHIC and at the LHC for a better description of the centrality dependent multiplicity density for all charged hadrons.

In the VISHNU simulations with MC-KLN initial conditions, we set a value of 0.16 for the QGP specific shear viscosity . Such combined setting in VISHNU calculations once nicely described the elliptic flow of , , and in Au + Au collisions [52] and Pb + Pb collisions [30]. Here, we continue to use it to further study the soft hadron data of strange and multistrange hadrons at both RHIC and LHC. For simplicity of the theoretical calculations, we neglect the bulk viscosity, net-baryon density, and the heat conductivity in the QGP system evolution.

#### 3. Spectra and Elliptic Flow

In Figure 1, we present the transverse momentum spectra of hadrons , , and in Au + Au collisions at = 200 GeV from the VISHNU hybrid model and compare these results with the STAR measurements. We observe that the VISHNU generally describes the -spectra but slightly overestimates the production of at all centrality classes. Our VISHNU results of at are about 40% lower than from STAR and about 20% lower than from STAR. This can be understood from the following. In our calculations, the production of is obtained from the original values of strong resonance decays from UrQMD of VISHNU. For the STAR measurements, the spectra are corrected for the feed-down of multistrange baryon weak decays (the feed-down contributions to the spectra from decays are negligible) [15]. Meanwhile, the STAR spectra are not corrected for the feed-down of decays from the channel of (for , the contribution from is via the channel of ). At LHC, it was found that the contribution from for is about 30% in VISHNU calculations [38]. Furthermore, we notice that STAR measurements of and are slightly larger than their corresponding antiparticles due to nonzero baryon density at this collision energy. In our calculations, however, zero net-baryon density is used, which leads to the same results between these (multi)strange hadrons and their antiparticle partners.