Latest predictions from the EbyE NLO EKRT model

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY-NC-ND 4.0 https://creativecommons.org/licenses/by-nc-nd/4.0/ Latest predictions from the EbyE NLO EKRT model © 2018 Published by Elsevier B.V. Published version Niemi, Harri; Eskola, Kari; Paatelainen, R.; Tuominen, K. Niemi, H., Eskola, K., Paatelainen, R., & Tuominen, K. (2019). Latest predictions from the EbyE NLO EKRT model. Nuclear Physics A, 982, 443-446. https://doi.org/10.1016/j.nuclphysa.2018.10.013 2019 XXVIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions (Quark Matter 2018) Latest predictions from the EbyE NLO EKRT model H. Niemia,b, K. J. Eskolaa,b, R. Paatelainenb,c, K. Tuominenb,c aUniversity of Jyv¨askyl¨a, Department of Physics, P.O. Box 35, FI-40014 University of Jyv¨askyl¨a, Finland bHelsinki Institute of Physics, P.O.Box 64, FI-00014 University of Helsinki, Finland cDepartment of Physics, University of Helsinki, P.O. Box 64, FI-00014 University of Helsinki, Finland Abstract We present the latest results from the NLO pQCD +saturation +viscous hydrodynamics (EbyE NLO EKRT) model. The parameters in the EKRT saturation model are fixed by the charged hadron multiplicity in the 0-5 % 2.76 TeV Pb+Pb collisions. The √s,Aand centrality dependence of the initial particle production follows then from the QCD dynamics of the model. This allows us to predict the √sand Adependence of the particle production. We show that our results are in an excellent agreement with the low-pTdata from 2.76 TeV and 5.02 TeV Pb+Pb collisions at the LHC as well as with the data from the 200 GeV Au+Au collisions at RHIC. In particular, we study the centrality dependences of hadronic multiplicities, flow coefficients, and various flow correlations. Furthermore, the nuclear mass number dependence of the initial particle production and hydrodynamic evolution can be tested in the 5.44 TeV Xe+Xe collisions at the LHC. To this end, we show our predictions for charged particle multiplicities, and in particular, show how the deformations of the Xe nuclei reflect into the flow coefficients. Keywords: heavy-ion collisions, perturbative QCD calculations, saturation, dissipative fluid dynamic 1. Introduction In the EKRT framework the initial conditions for hydrodynamical evolution in heavy-ion collisions are calculated by using NLO perturbative QCD and collinear factorization together with a saturation conjecture that controls the transverse energy production through a semi-hard scale psat [1, 2]. The saturation momentum is a function of √sand the nuclear mass number, and depends on the transverse coordinate through the product of nuclar thickness functions TA[3, 4], psat =psat(TATA,√s,A,Ksat), where Ksat is fixed by the charged particle multiplicity in 0 −5 % 2.76 TeV Pb+Pb collisions. Once Ksat is fixed, the initial conditions can be computed for any √sand A, as long as they are sufficiently large, so that the psat remains perturbative. The local formation time can be estimated as τs(r)=1/psat(r) and the local energy density at the formation time is then given by e(r,τ s(r)) =Ksat π[psat(r)]4[5]. This profile is then evolved to a common time τ0=1/pmin sat =0.2 fm by using 0+1D Bjorken hydrodynamics. The evolved energy density profile can then be used as an initial condition for the full fluid dynamical evolution. The subsequent evolution of the system is described by a boost-invariant Israel-Stewart type of dissipative fluid dynamics with the coefficients of the non-linear terms from Refs. [6, 7]. The kinetic freeze-out is Available online at www.sciencedirect.com Nuclear Physics A 982 (2019) 443–446 0375-9474/© 2018 Published by Elsevier B.V. www.elsevier.com/locate/nuclphysa https://doi.org/10.1016/j.nuclphysa.2018.10.013 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Fig. 1. The tested temperature dependencies of η/s(Left). The centrality dependence of vnin 200 GeV Au+Au collisions (Middle), and 2.76 TeV Pb+Pb collisions (Right). The experimental data are from ALICE [13] and STAR [14, 15, 16]. Tdec =100 MeV. The chemical freeze-out at Tchem =175 MeV is encoded into the equation state, for which we use the s95p-PCE-v1 parametrization [8, 9]. We neglect the bulk viscosity and set the initial values of shear-stress tensor and transverse velocity to zero. The remaining free input is the parametrization of the temperature dependence of the shear viscosity to entropy density ratio, η/s(T). As discussed in detail in Ref. [10], the nuclear shapes and the event-by-event fluctuations enter the calculation through TA. The event-by-event TAis computed by sampling the nucleon positions from the Woods-Saxon parametrization of the nucleon density. For each nucleon we then set a gaussian transverse density profile, and the nuclear TAis the sum of these nucleon thickness functions. We take the Pb and Au nuclei to be spherically symmetric, but as in Ref. [11], for the Xe nuclei we take into account the nuclear shape deformation, described by the parameters β2=0.163 and β4=−0.003 from Ref. [12]. 2. Results The parametrizations of η/s(T) are constrained by the flow coefficients vnand various flow correlators in 200 GeV Au+Au and 2.76 TeV Pb+Pb collisions [10]. The η/s(T) parametrizations that give the overall best agreement with these data are shown in Fig. 1 (Left), and the corresponding vnare shown in Figs. 1 (Middle) and 1 (Right), respectively. In Fig. 2 we show various correlation measures between vnand vm, defined through so called normalized symmetric cumulants, nsc(n,m)=v2 nv2 m/v2 nv2 m−1, where the angular brackets denote the event averaging, accounting the proper weights of the event multiplicity [17]. The best agreement with the correlators is obtained with the same η/s(T) parametrizations as the vnthemselves, thus the consistency between the experimental data and the fluid dynamical behavior is excellent. Armed with the η/s(T) parametrizations and the corresponding values of Ksat that were fixed in Ref. [10] our framework is closed, and we can predict the low-pThadronic observables for 5.023 TeV Pb+Pb [18] and 5.44 TeV Xe+Xe [19] collisions that were measured recently. In Fig. 3 we show the centrality dependence of the charged hadron multiplicity for all the systems we are considering. The predictions are in excellent agreement with the measured multiplicities. The predicted vnin 5.023 TeV Pb+Pb collisions are shown in Fig. 4 as the ratios to vnin the 2.76 TeV Pb+Pb collisions. The data is from the ALICE Collaboration [25]. The predicted slight increase of vnis consistent with the measurement. Finally, in Fig. 5 we show the ratio of our predicted vnfor the 5.44 Xe+Xe collisions to vnin 5.023 TeV Pb+Pb collisions compared to the ALICE data [26]. The Xe nuclei are not spherically symmetric, and as a result the initial conditions are modified compared to the spherical case, especially in more central collisions, and moreover the modified initial densities then reflect through the fluid dynamical evolution to the final flow coefficients [11]. In the figure we show both the cases: with and without accounting for the nuclear deformation. As can be seen from the figure, vnin central collisions are enhanced compared to the vnin 5.023 TeV Pb+Pb collisions regardless of whether we include the Xe deformation or not. However, with the deformation the enhancement of the elliptic flow, v2, is much stronger, and it is clearly necessary to include the deformation in order to describe the experimental data. For larger nthe effect of deformation is much weaker. H. Niemi et al. / Nuclear Physics A 982 (2019) 443–446444 Fig. 2. The normalized symmetric cumulants in 2.76 TeV Pb+Pb collisions. The data are from Ref. [17]. 0 10 20 30 40 50 60 70 80 centrality [%] 102 103 dNch/dη|η|<0.5 Xe+Xe η/s =0.20 η/s =param1 ALICE 5.023 TeV ALICE 5.44 TeV Xe ALICE 2.76 TeV STAR PHENIX Fig. 3. Centrality dependence of the charged hadron multiplicity. The experimental data are from ALICE [20, 21, 22], STAR [23] and PHENIX [24]. 20 40 centrality [%] 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 vn{2}(5.023 TeV)/vn{2}(2.76 TeV) (a) n=2 η/s =0.20 η/s =param1 ALICE 20 40 centrality [%] pT=[0.2...5.0] GeV LHC Pb + Pb (b) n=3 20 40 centrality [%] (c) n=4 Fig. 4. The ratio of vnbetween 2.76 TeV and 5.023 TeV Pb+Pb collisions. The data are from Ref. [25]. H. Niemi et al. / Nuclear Physics A 982 (2019) 443–446 445 20 40 60 centrality [%] 0.9 1.0 1.1 1.2 1.3 1.4 rn (a) rn=vn{2}(Xe+Xe,5.44 TeV) vn{2}(Pb+Pb,5.02 TeV) n=2 η/s =0.20 η/s =param1 symmetric Xe 20 40 60 centrality [%] pT=[0.2...3.0] GeV (b) n=3 ALICE 20 40 60 centrality [%] (c) Deformed Xe : β2=0.162 β4=−0.003 n=4 Fig. 5. The ratio of vnbetween 5.023 TeV Pb+Pb and 5.44 TeV Xe+Xe collisions. The data are from Ref. [26]. As a conclusion, we have demonstrated that our framework of EKRT initial conditions together with the dissipative fluid dynamical evolution describes a large class of low-pTobservables in a wide range of collision energies. Especially, we have shown that once the framework is fixed at 200 GeV Au+Au and 2.76 TeV Pb+Pb collisions, we can predict the √sand Adependence of the soft observables and describe all these systems with the same η/s(T), which is a necessary requirement to demonstrate a fluid dynamical behavior. In particular, the measurement of the Xe+Xe collisions is a very good test of the Adependence of the initial particle production and fluid dynamical behaviour. The measured vnshow exactly the behaviour we expect from the fluid dynamical response to the modified geometry due to the nuclear deformations. 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