Beam-energy and collision-system dependence of the linear and mode-coupled flow harmonics from STAR
aa r X i v : . [ nu c l - e x ] F e b Nuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
Beam-energy and collision-system dependence of the linearand mode-coupled flow harmonics from STAR
Niseem Magdy for the STAR Collaboration Department of Physics, University of Illinois at Chicago, Chicago, Illinois 60607, USA
Abstract
Recent measurements and hydrodynamic model calculations suggest that the higher-order flow coe ffi cients v and v have two contributions: a linear contribution driven by the initial-state eccentricities, ε n , and a mode-coupled contribu-tion derived from the lower-order eccentricity coe ffi cients ε and ε . Measurements of these two contributions to v and v provide crucial insights to discern initial-state models and to constrain the temperature-dependent specific shear vis-cosity, η/ s , of the plasma produced in heavy-ion collisions. In this work, we have employed the two-subevents cumulanttechnique to provide the first beam-energy and collision-system dependence of the linear and mode-coupled contribu-tions to the higher-order flow harmonics. Our results are shown and discussed for several centrality intervals for U + Ucollisions at √ s NN =
193 GeV, Au + Au collisions at √ s NN = + Au collisions at √ s NN =
200 GeV.The results are compared with similar studies performed by the ALICE experiment at LHC.
Keywords:
Collectivity, correlation, shear viscosity
PACS:
1. Introduction
Ongoing investigations of the matter produced in heavy-ion collisions at the Relativistic Heavy IonCollider (RHIC) and the Large Hadron Collider (LHC) indicate that an exotic state of matter called Quark-Gluon Plasma (QGP) is produced. Many of these studies are aimed to understand the dynamical evolutionand transport properties of QGP [1, 2].The measurements of the azimuthal anisotropy of the particle production called anisotropic flow havebeen used in various studies to explain the viscous hydrodynamic response to the initial spatial distributionin energy density, created in the early stages of the collision [3, 4].The anisotropic flow can be described via the Fourier expansion [5] of the azimuthal angle distributionof the particle production: dNd φ = N π + X n = V n e − in φ , (1) [email protected] / Nuclear Physics A 00 (2020) 1–4 where V n = v n exp( in Ψ n ) is the n th complex flow vector, Ψ n represents the flow vector direction, and v n is theflow vector magnitude. The azimuthal anisotropic flow harmonic v is known as directed flow, v as ellipticflow, and v as triangular flow, etc.To a good degree, the lower-order flow harmonics v and v are linearly related to the initial-stateanisotropies ε and ε respectively [6]. However, the higher-order flow harmonics, v n > , arising from lin-ear response to the same-order initial-state anisotropies along with non-linear response to the lower-ordereccentricities ε and / or ε [7]. Consequently, the full benefit of the higher-order flow harmonics for η/ s extraction [8] benefits form a robust separation of their linear and non-linear contributions.The higher-order flow harmonic V can be expressed as: V = V Linear4 + V Non − linear4 , (2) V Non − linear4 = χ , V V , (3)where χ , is the non-linear response coe ffi cients. The value of χ , constrains the magnitude of V Non − linear4 .Also the magnitude of V Non − linear4 encodes the correlations between the flow symmetry planes Ψ and Ψ .In this work, we employ the multiparticle cumulant method [9] to measure the p T -integrated inclusive,non-linear and linear higher-order flow harmonic v in collisions of U + U at √ s NN =
193 GeV, Cu + Au at √ s NN =
200 GeV and Au + Au at several beam energies.
2. Method
The STAR data of charged particles were analyzed with the multiparticle cumulant technique [10, 9].The framework for the standard cumulant method is discussed in Ref. [10]; its extension to the subeventsmethod is reported in Ref. [9]. In order to minimize the non-flow correlations in the two-subevent method,the cumulants are constructed from two-subevents which are separated in η . Thus, the constructed multipar-ticle correlations can be written as: v n = hh cos( n ( ϕ A − ϕ B )) ii / , (4) C n + m , n , m = hh cos(( n + m ) ϕ A − n ϕ B − m ϕ B ) ii , h v n v m i = hh cos( n ϕ A + m ϕ A − n ϕ B − m ϕ B ) ii , where, hh ii represents the average over all particles in the event, which are then averaged over event sample, k , n and m are harmonic numbers and ϕ i is the i th particle’s azimuthal angle. For the two-subevent method,subevent A and subevent B are required to have a minimum ∆ η > . η A > . η B < − . v can beexpressed as: v Non − linear4 = C , / q h v v i , (5) v Linear4 = q ( v Inclusive4 ) − ( v Non − linear4 ) . Equation (5) assumes that the linear and non-linear contributions in v are independent [11], which is acorrect approach if the correlation between the lower- ( n = ,
3) and higher-order ( n >
3) flow coe ffi cientsis weak.
3. Results
A centrality dependencies of the inclusive, linear and non-linear v in the p T range from 0 . . / c forAu + Au collisions at √ s NN =
200 GeV are shown in Fig. 1. Our study indicates that the v Linear4 depends
Nuclear Physics A 00 (2020) 1–4 v Centrality (%)
STAR PreliminaryAu+Au 200 GeV
Inclusive Non-linearLinear
Fig.
1. The inclusive, non-linear and linear higher-order flow harmonic v using the two-subevent cumulant method as a functionof centrality in the p T range from 0 . . / c are shown for Au + Au collisions at √ s NN =
200 GeV. The respective systematicuncertainties are shown as open boxes. (a)Inclusive STAR Preliminary
Centrality (%) v
0 20 40 60(b)Non-linear
Centrality (%)
0 20 40 60(c)Linear
Centrality (%)
Pb+Pb 2.76 TeVAu+Au 200 GeVAu+Au 54.4 GeV
Fig.
2. The inclusive, non-linear and linear higher-order flow harmonic v using the two-subevent cumulant method as a functionof centrality in the p T range from 0 . . / c are shown for Au + Au collisions at √ s NN =
200 and 54.4 GeV. The respectivesystematic uncertainties are shown as open boxes. The results are compared with the LHC measurements in the p T range from 0 . . / c for Pb + Pb collisions at √ s NN = (a)InclusiveSTAR Preliminary Centrality (%) v U+U Au+AuCu+Au
0 20 40 60(b)Non-linear
Centrality (%)
0 20 40 60(c)Linear
Centrality (%)
Fig.
3. The inclusive, non-linear and linear higher-order flow harmonic v are shown for U + U collisions at √ s NN =
193 GeV, andAu + Au and Cu + Au collisions at √ s NN =
200 GeV. The presented results are measured using the two-subevent cumulant method as afunction of centrality in the p T range from 0 . . / c . The respective systematic uncertainties are shown as open boxes. weakly on the collision centrality and it dominates over the non-linear contribution to the inclusive v incentral collisions.Figure 2 compares the centrality dependence of the inclusive, linear and non-linear v in the p T rangefrom 0 . . / c for Au + Au collisions at √ s NN =
200 and 54.4 GeV. For both energies we observe thatthe linear mode of v has a weak centrality dependence, and it is the dominant contribution to the inclusive v in central collisions. The preliminary results are compared with similar LHC measurements in the p T / Nuclear Physics A 00 (2020) 1–4 range from 0 . . / c for Pb + Pb collisions at √ s NN = ff erence of v magnitudes between Au + Au collisions at √ s NN = + Pb collisions at √ s NN = ff erence in the viscous e ff ects between those energies.The preliminary results for U + U collisions at √ s NN =
193 GeV, and Au + Au and Cu + Au collisions at √ s NN =
200 GeV are shown in Fig. 3. The magnitudes and trends for both inclusive and non-linear v showa weak system dependence, albeit with more visible di ff erences between Cu + Au and Au + Au than betweenU + U and Au + Au.
4. Summary
In summary, we have used the cumulant method to measure the inclusive, linear and non-linear v asa function of collision centrality in U + U collisions at √ s NN =
193 GeV, Cu + Au at √ s NN =
200 GeV andAu + Au at several beam energies. The measurements show the expected characteristic dependence of theinclusive, linear and non-linear v on centrality, system size and beam energy. Our study indicates that thelinear contribution to the inclusive v dominates over the non-linear contribution in central collisions for allpresented energies and systems. These newly presented measurements may give extra constraints to testdi ff erent initial-state models and assist to accurate extraction of the QGP specific shear viscosity. Acknowledgments
The author thank Prof. ShinIchi Esumi for the very successful discussions. This research is supportedby the US Department of Energy under contract DE-FG02-94ER40865
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