Latest results from the EbyE NLO EKRT model

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Latest results from the EbyE NLO EKRT model Eskola, Kari; Niemi, Harri; Paatelainen, Risto; Tuominen, Kimmo Eskola, K., Niemi, H., Paatelainen, R., & Tuominen, K. (2017). Latest results from the EbyE NLO EKRT model. Nuclear Physics A, 967, 313-316. https://doi.org/10.1016/j.nuclphysa.2017.04.038 2017 Latest results from the EbyE NLO EKRT model K. J. Eskolaa,b, H. Niemic, R. Paatelainena, K. Tuominend,b aUniversity of Jyvaskyla, Department of Physics, P.O.B. 35, FI-40014 University of Jyvaskyla, Finland bHelsinki Institute of Physics, P.O.B. 64, FI-00014 University of Helsinki, Finland cInstitut f¨ur Theoretische Physik, Johann Wolfgang Goethe-Universit¨at, Max-von-Laue-Str. 1, D-60438 Frankfurt am Main, Germany dDepartment of Physics, P.O.B. 64, FI-00014 University of Helsinki, Finland Abstract We review the results from the event-by-event next-to-leading order perturbative QCD +saturation +viscous hydrodynamics (EbyE NLO EKRT) model. With a simultaneous analysis of LHC and RHIC bulk observables we systematically constrain the QCD matter shear viscosity-to-entropy ratio η/s(T), and test the initial state computation. In particular, we study the centrality dependences of hadronic multiplicities, pTspectra, flow coefficients, relative elliptic flow fluctuations, and various flow-correlations in 2.76 and 5.02 TeV Pb+Pb collisions at the LHC and 200 GeV Au+Au collisions at RHIC. Overall, our results match remarkably well with the LHC and RHIC measurements, and predictions for the 5.02 TeV LHC run are in an excellent agreement with the data. We probe the applicability of hydrodynamics via the average Knudsen numbers in the space-time evolution of the system and viscous corrections on the freeze-out surface. Keywords: heavy-ion collisions, next-to-leading order perturbative QCD calculations, saturation, dissipative fluid dynamics 1. NLO EbyE EKRT model and its tests The EKRT model [1, 2] rests on the idea that primary particle production in high energy heavy-ion collisions is dominated by few-GeV gluons, minijets [3], whose production rates are computable from collinear factorization of perturbative QCD (pQCD) but controlled by the phenomenon of saturation locally in the transverse plane [4, 5, 6]. The produced minijet densities can then be converted into initial conditions for relativistic fluid dynamics simulations. In NLO pQCD, the infrared- and collinear-safe quantity computed here is the transverse energy ETcarried by the minijets into a mid-rapidity window Δy[7, 5] per transverse area d2rin A+Acollisions at cms-energy √sNN and impact parameter b, dET d2r(p0,√sNN,A,Δy,r,b;β)pQCD =TA(r+b/2)TA(r−b/2)σETp0,Δy,β saturation =Ksat πp3 0Δy,(1) where the transverse momentum cut-offp0∼few GeV, and TAis the nuclear thickness function. The NLO quantity σETp0,Δy,β is computed using collinear factorization and the subtraction method [8]. It contains the CTEQ6M parton distributions [9] with EPS09s nuclear effects [10], 2 →3 and UV-renormalized 2 →2 parton scattering matrix elements [11], and the measurement functions to define the ET. The minimum ET in Δyis controlled by the parameter β∈[0,1], fixed to 0.8 here [5]. Saturation here is the limit where ET Available online at www.sciencedirect.com Nuclear Physics A 967 (2017) 313–316 0375-9474/© 2017 The Author(s). Published by Elsevier B.V. www.elsevier.com/locate/nuclphysa http://dx.doi.org/10.1016/j.nuclphysa.2017.04.038 This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). production from (n>2) →2 parton processes starts to dominate over the usual 2 →2 ones. This can be cast into the form of the saturation condition appearing on the r.h.s. of Eq. (1), where Ksat is a free parameter [5]. Equation (1) gives the saturation momentum p0=psat(√sNN,A,r,b;β, Ksat) locally in the transverse plane. With a formation time τs(r)=psat(r)−1the initial local energy density is then e(r,τ s(r)) =dET d2r 1 τs(r)Δy=Ksat π[psat(r)]4.(2) The observation [6, 12] enabling the NLO EbyE EKRT model of Ref. [2] is that the obtained psat(r,b)≈ psat(TATA) which dependence can be parametrized, see Eq. 29 in [2]. Then the TAs can be made to fluctuate EbyE: we sample the nucleon positions from the standard Woods-Saxon density, setting a Gaussian gluon thickness function of a width σ=0.43 fm [14] around each nucleon, and then computing the TAas a sum of these gluon clouds. Thus, the fluctuations of TAdetermine how e(r,τ s(r)) fluctuates here EbyE. Finally, to start our hydro simulations at a constant time, we evolve the e-profile from τs(r)toτ0=1/pmin sat =0.2fm using 0+1 D Bjorken hydrodynamics. At the edges of the system, we assume a binary e-profile, e∝TATA. With such initial conditions, we then describe the spacetime evolution of QCD matter event by event, using 2nd-order dissipative relativistic 2+1 D hydro with transient fluid-dynamics equation of motion for the shear-stress tensor πμν from Refs. [15, 16]. The transverse flow and πμν are initially zero. Our equation of state is s95p-PCE-v1 [17], with chemical decoupling at Tchem =175 MeV. Kinetic freeze-out is at Tdec =100 MeV, and on this surface we assume, as usual, that the viscous δf-corrections are ∝pμpνπμν.We neglect the bulk viscosity and heat conductivity. We study the Tdependence of η/s(T) with the parametrizations of Fig. 1a, all of which are designed to reproduce the flow coefficients vn{2}measured in 2.76 TeV Pb+Pb collisions at the LHC, as shown in Fig. 1b. The parameter Ksat is fixed separately for each η/s(T) parametrization, by using the dNch/dη(0−5%) measured by ALICE in 2.76 TeV Pb+Pb collisions (Fig. 3a). B C D Fig. 1. (a) The tested η/s(T) parametrizations. Flow coefficients vn{2}vs. ALICE data [18] in 2.76 TeV Pb+Pb collisions at the LHC (b), and v2{2},v3{2}and v4{3}vs. STAR data [19, 20, 21] in 200 GeV Au+Au collisions (c). From [13, 2]. We have extensively tested the NLO EbyE EKRT model in [2], arriving at a very good simultaneous description of the centrality dependences of charged hadron multiplicities, pTspectra, and flow coefficients in 2.76 TeV Pb+Pb collisions at the LHC and 200 GeV Au+Au at RHIC. As seen in Fig. 1c, the RHIC vns favor small hadronic viscosities, η/s(T)=0.2 (blue) and param1 (black). Also the correlations of 2 and 3 event-plane angles measured by ATLAS systematically favor these two parametrizations, see Fig. 2a [2]. Furthermore, these constraints are obtained in the centrality region where the δfeffects remain small in these observables [2]. Relative EbyE fluctuations of v2measured by ATLAS provide a stringent η/s-independent test for the computed initial states. The EKRT model passes also this test remarkably well, demonstrating the necessity of a hydro evolution in understanding the centrality systematics of this observable [2]. As a measure of our hydro validity, we plot in Fig. 2f also (i) the average Knudsen numbers Kn, expansion rate (θ=∂μuμ) per thermalization time (τπ=5η/(e+p)) averaged over entropy density throughout the evolution (T>100 MeV), and (ii) the shear stress over pressure πμνπμν/paveraged over the entropy flux through the freeze-out surface. This reflects the average δfcorrections in the end of the evolution. The facts that these indicators increase towards peripheral collisions only gradually and that Kn=O(1) speak for the hydro validity at least up to 50% centralities. Towards peripheral collisions, Knincreases due to the increasing relative weight of the early stages where Knis large (see the T>180 MeV curve). K.J. Eskola et al. / Nuclear Physics A 967 (2017) 313–316314 B C D E F G Fig. 2. Centrality dependence of various correlators and Knudsen number in 2.76 TeV Pb+Pb collisions. (a) Correlation of the event-plane angles Ψ2and Ψ4vs. ATLAS data [23]. From [2]. (b) Normalized cumulants SC(4,2)/v2 4v2 2vs. ALICE data [24]. (c) Same for SC(3,2)/v2 3v2 2. (d) SC(4,2)/v2 4v2 2in one low-pTand one high-pTinterval, computed with our two best-fit η/s parametrizations. (e) Low-to-high-pTratio of SC(4,2)/v2 4v2 2. (f) Average Knudsen numbers Knin our hydro evolution (red, green), and average shear stress over pressure π/pon the freeze-out surface (black), computed with the param1 η/sparametrization. 2. Further predictions from the EbyE NLO EKRT model We have made a series of predictions from the EbyE NLO EKRT model without any further tuning. For ALICE, we have computed the symmetric 2-harmonic 4-particle cumulants, SC(m,n)=cos(mφ1+nφ2− mφ3−nφ4) =v2 mv2 n−v2 mv2 nnormalized by v2 mv2 nshown in Fig. 2b,c. Our best-fit η/sparametrizations predict rather well the positive correlation seen by ALICE [24] in SC(4,2) and also the trend of the negative correlation in SC(3,2). We emphasize, however, the importance of a 1-to-1 comparison: we expect that once we include the multiplicity weighting assumed in the ALICE analysis, our prediction will be systematically closer to the data. In Fig. 2d we show a prediction of the pTdependence of SC(4,2)/v2 4v2 2. Fig. 2e in turn suggests that the low-to-high-pTratios of these normalized correlators might be able to distinguish between our best-fit η/sparametrizations. Similarly, we have provided the STAR collaboration with our predictions for the centrality dependence of mixed harmonic correlators Cm,n,m+n=cos(mφ1+nφ2−(m+n)φ3).As shown in [22], our best-fit parametrizations reproduce the C2,2,4rather well. However, we underestimate the measured C2,3,5, which we believe is due to large δfeffects in this observable, possibly combined also with non-flow and rapidity effects which we cannot consider, yet. Further studies on this are ongoing. Thanks to the predictive power of the EKRT model, we have also made predictions for the 5.02 TeV Pb+Pb run at the LHC [13]. Figure 3 shows our predictions for the multiplicity and flow-coefficient ratios. In the latter, notice the slight increase with increasing n. Again, as seen in the figure, the EbyE NLO EKRT model fairs very well in the data comparison. To conclude, the EbyE NLO EKRT model [2] explains consistently the bulk observables and various correlators at mid-rapidity in LHC and RHIC heavy-ion collisions. Its predictive power in cms-energy, centrality and nuclear mass number has been demonstrated with various observables. Via a multi-energy and multi-observable analysis we have managed to constrain the η/s(T) ratio, for which two best-fit parametrizations have been identified. Similar results have been found also in Ref. [31]. Systematic further tests of the hydro results validity are, however still needed, especially in the case of more complicated correlators, as well as more work for including further dissipative phenomena. Acknowledgments. K.J.E. is supported by the Academy of Finland, Project 297058, and H.N. by the EU’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement no. 655285. K.J. Eskola et al. / Nuclear Physics A 967 (2017) 313–316 315 B C D E F Fig. 3. EbyE NLO EKRT model predictions for 5.023 TeV Pb+Pb collisions [13]. (a) Centrality dependence of charged particle multiplicity, vs. ALICE data [25, 26]. 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