Linear and non-linear flow modes of charged and identified particles in Pb--Pb collisions at s NN − − − √ =5.02 TeV with ALICE
NNuclear Physics A 00 (2020) 1–4
NuclearPhysics A / locate / procedia XXVIIIth International Conference on Ultrarelativistic Nucleus-Nucleus Collisions(Quark Matter 2019)
Linear and non-linear flow modes of charged and identifiedparticles in Pb–Pb collisions at √ s NN = Jasper Parkkila for the ALICE Collaboration
CERN, Route de Meyrin, 1211 Geneva, Switzerland
Abstract
The higher order harmonic flow observables v n ( n >
3) and their non-linear responses to the initial state anisotropy havethe strong potential to constrain shear and bulk viscosity to entropy ratios because of di ff erent sensitivities for variousstages of heavy-ion collisions. The measurements of the flow coe ffi cients and the non-linear coe ffi cients up to the ninthand fifth harmonic, respectively, are presented in Pb–Pb collisions at √ s NN = p T -di ff erential non-linear flow modes for π ± , K ± , p + ¯p, K s , Λ + ¯ Λ s and φ are presented. The results arecompared to the same measurements at 2.76 TeV and calculations from state of the art hydrodynamic models. Keywords: higher harmonic, flow modes, non-linear, identified
1. Introduction
Quark-Gluon Plasma (QGP), the state of the matter that exists at extremely high temperatures and energydensities, is studied at the LHC [1]. One of the primary goals of heavy-ion collision programs is to studythe properties of this strongly interacting matter by measuring observables, such as the anisotropic flow thatarises from the hydrodynamic expansion of the initial state spatial anisotropies in the energy density profile.As a result, anisotropic flow measurements through multi-particle azimuthal correlations can probe initialstate fluctuations and important properties of the shear viscosity to entropy density ratio ( η/ s ), bulk viscosityto entropy ratio ( ζ/ s ) and equation of state.The second and third harmonic coe ffi cients of the anisotropic flow are known to follow an approximatelylinear relation to their corresponding eccentricity in the initial conditions, with v n ∝ ε n ( n = , v n is the magnitude of the n th harmonic flow vector V n . However, in higher harmonics n > V n are induced not only by their corresponding n -th order eccentricityvector, but also lower order harmonics. It has been shown [2] that the higher order flow can be expressedas a combination of linearly correlated contribution V n L and one or more contributions from the lower orderharmonics: V = V + χ , V , V = V + χ , V V , V = V + χ , V + χ , V + χ , V V L ,. . . (1) Email address: [email protected] () a r X i v : . [ nu c l - e x ] M a r Jasper Parkkila for the ALICE Collaboration / Nuclear Physics A 00 (2020) 1–4 v v (×3.0)ALICE Pb-Pb s NN =5.02TeV0.4<| |<0.8, 0.2< p T <5.0GeV/c1.01.20.0000.0050.0100.0150.020 v ALICE v n EKRT, / s =0.20, / s =0 EKRT, / s ( T ), / s =0 v (×2.0) AMPT, / s =0.08, / s =0 TRENTo, / s ( T ), / s ( T ) IP-Glasma, / s =0.095, / s ( T )0 10 20 30 40 50 600.751.001.25 0 10 20 30 40 50 60 Centrality (%) v n T h e o r y / D a t a v n T h e o r y / D a t a ALICE Preliminary
Fig. 1. v n with hydrodynamical model calculations. ALICE Pb-Pb s NN =5.02TeV0.4<| |<0.8, 0.2< p T <5.0GeV/cCentralityn=2...6 Centralityn=7...9
Centralityn=7...9 n v n ALICE Preliminary
Fig. 2. v n as a function of the harmonic order n for various centralityintervals. where χ n , mk , called non-linear flow mode coe ffi cient, characterizes the non-linear flow mode induced by thelower order harmonics. The magnitude of non-linear mode for the fourth harmonic, v , ≡ χ , (cid:113) (cid:104) v (cid:105) = (cid:60)(cid:104) V ( V ∗ ) (cid:105)(cid:104) v (cid:105) is obtained with a projection of V onto the second harmonic plane Ψ . The measurement of thisquantity is performed using the subevent method, where the event is divided into two subevents separatedby a pseudorapidity gap | ∆ η | > .
8. The subevent method e ff ectively suppresses the non-flow contributionsfrom short-range correlations unrelated to the common symmetry plane. For subevent A, the multi-particlecorrelation is v A4 , = (cid:104)(cid:104) cos(4 ϕ A1 − ϕ B2 − ϕ B3 ) (cid:105)(cid:105) / (cid:104)(cid:104) cos(2 ϕ A1 + ϕ A2 − ϕ B3 − ϕ B4 (cid:105)(cid:105) , while for subevent B the’A’ and ’B’ in the aforementioned expression are interchanged. The final result is the average of the resultsfrom the two subevents. In a p T -di ff erential analysis, ϕ is taken from a certain p T region ( ϕ ( p T )) or is of aspecific particle species.In these proceedings the measurements of the higher order flow up to v are reported in Pb–Pb collisionsat √ s NN = .
02 TeV [3]. Furthermore, measurements of the non-linear flow mode coe ffi cients χ n , mk arepresented up to the fifth harmonic, among with comparisons to various state of the art hydrodynamicalcalculations. The high-order harmonic coe ffi cients are expected to have good sensitivities to the hydrodynamicparameters such as η/ s and ζ/ s , and thus improve the constraints on these transport properties. The p T -di ff erential non-linear flow modes are presented for the identified π ± , K ± , p + ¯p, K s , Λ+ ¯ Λ s and φ [4]. Suchmeasurements yield additional constraints for the initial conditions, η/ s and ζ/ s , and revealing informationabout di ff erent particle production mechanisms.
2. Analysis Details
The data sample consists of about 42 million minimum-bias Pb–Pb collisions at √ s NN = .
02 TeV, recordedby ALICE [5] in 2015. The trigger requires coincidence of signals from the two scintillator arrays, V0A andV0C [5]. The track reconstruction is based on information from the Time Projection Chamber (TPC) [5]and the Inner Tracking System (ITS) [5]. For unidentified flow, only particle tracks within the transversemomentum interval 0 . < p T < . / c and pseudorapidity range 0 . < | η | < . | ∆ η | > . π ± ), kaons (K ± ), (anti-)protons(p + ¯p). For decaying particles K s , Λ + ¯ Λ s and φ , the invariant mass method is employed. A minimum 80%purity is maintained for all particle species. The sub-event method (without η -separation) is applied and thepossible remaining non-flow is considered in the systematical uncertainty. The observables in this analysisare measured with multi-particle correlations obtained using the generic framework [6] for anisotropic flowanalysis. asper Parkkila for the ALICE Collaboration / Nuclear Physics A 00 (2020) 1–4
4, 22
EKRT, / s = 0.20, / s = 0 EKRT, / s ( T ), / s = 0 AMPT, / s = 0.08, / s = 0 TRENTo, / s ( T ), / s ( T ) IP-Glasma, / s = 0.095, / s ( T )
5, 23 (×0.5)ALICE Pb-Pb s NN = 5.02 TeV0.4 < | | < 0.8, 0.2 < p T < 5.0 GeV/c ALICE 5.02 TeV 2.76 TeV (Phys.Lett.B773 68-80)
Centrality (%)
ALICE Preliminary n , m k T h e o r y / D a t a Fig. 3. Non-linear flow mode coe ffi cients. The new measurements are presented as black squares, while the lower energy results are inred [11]. The model calculations are shown in various colored bands.
3. Results
In Fig.1 the flow coe ffi cients are presented up to v among with hydrodynamical calculations. IP-Glasmawith viscous hydrodynamics describes the data best for n = n =
3, while EKRT( η/ s = .
2) has thebest agreement for n = n =
5. Likewise, TRENTo has a good agreement for n = n = ffi cients in various centrality bins, where v and v are measured forthe first time at the LHC energies. The magnitudes of v and v are compatible with v within uncertainties.The decrease of magnitude as a function of harmonic n can be characterized by a relation v n ∝ e − k (cid:48) n up to v . The e ff ect might be described by viscous damping based on studies in Ref. [7, 8]: a higherfrequency waveform propagating through the medium is more strongly damped than the lower frequenciesuntil freeze-out takes place. The relation is observed as partially broken at very high harmonics, where thedamping in magnitude is no longer exponential. As predicted by the acoustic model [7], the harmonic phaseoscillation itself might contribute to the magnitude of the flow coe ffi cients at the freeze-out, which couldresult in enhancement of magnitude at very high harmonics.The results of the non-linear flow mode coe ffi cients χ , and χ , are presented in Fig. 3. For bothcoe ffi cients, the overall centrality dependence is subtly decreasing, and the χ , is about twice in magnitudecompared to χ , . The results agree with those at √ s NN = .
76 TeV. Discrepancies between data andmodel calculations are clearly visible. EKRT( η/ s = .
2) and TRENTo have the best agreement with thedata. EKRT( η/ s ( T )) and IP-Glasma both overestimate the data, while AMPT underestimates χ , . Thesensitivity of the higher order χ , to model parameterizations at freeze-out temperature is more prominentthan for χ , , and is further pronounced in even higher harmonics [9]. None of the models reproduce thecentrality dependence of the non-linear flow mode coe ffi cients within uncertainties.Finally, Fig. 4 presents the p T -di ff erential non-linear flow modes for the identified hadrons in 10-20%centrality class. For all v n , mk , a mass ordering v π ± n , mk > v K n , mk > v pn , mk ≈ v Λ n , mk ≈ v φ n , mk is observed up to p T = . / c , known to be caused by an interplay between the radial flow and the non-linear response.At p T > . / c , particle type grouping is recognized with baryon flow larger than the meson flow v Λ n , mk ≈ v pn , mk > v π ± n , mk ≈ v K n , mk . Such behaviour has also been observed for flow coe ffi cients v n in [10], whichimplies the particle production primarily by quark coalescence, meaning that the flow is generated duringthe partonic phase of the collision process.
4. Summary
The results for the higher order anisotropic flow coe ffi cients v n and the non-linear flow mode coe ffi cients χ n , mk are presented up to ninth and fifth harmonic, respectively. The magnitude of flow coe ffi cients decreasesexponentially as the harmonic n increases up to n =
7. For n >
7, this is no longer clearly visible. Futuremeasurements of v n based on the large Pb–Pb collisions data set taken in 2018 will allow to investigate Jasper Parkkila for the ALICE Collaboration / Nuclear Physics A 00 (2020) 1–4
ALI-PREL-324076 ALI-PREL-324091ALI-PREL-324106 ALI-PREL-324122
Fig. 4. Non-linear flow modes of identified hadrons for v , , v , , v , and v , . damping of harmonics at n >
7. The measurements of the non-linear flow mode coe ffi cients show theincreased non-linear response in higher harmonic. Out of the presented model comparisons EKRT( η/ s = p T -di ff erential non-linear flow modes for identified hadrons were presentedup to the sixth harmonic. The measurements show a clear mass ordering at p T < . / c . At higher p T range, particle type grouping is observed. Measurements of identified flow are an important additionalconstraint, as non-linear flow of various particle species can provide information especially on late-stagehadronic interactions and mechanisms of particle production. These new measurements allow the transportproperties of the QGP to be better constrained. References [1] S. A. Voloshin, A. M. Poskanzer, R. Snellings, Collective phenomena in non-central nuclear collisions, Landolt-Bornstein 23(2010) 293–333. arXiv:0809.2949 , doi:10.1007/978-3-642-01539-7_10 .[2] F. G. Gardim, F. Grassi, M. Luzum, J.-Y. Ollitrault, Mapping the hydrodynamic response to the initial geometry in heavy-ioncollisions, Phys. Rev. C85 (2012) 024908. arXiv:1111.6538 , doi:10.1103/PhysRevC.85.024908 .[3] S. Acharya, et al., Linear and non-linear flow modes of charged hadrons in Pb-Pb collisions at √ s NN = arXiv:2002.00633 .[4] S. Acharya, et al., Non-linear flow modes of identified particles in Pb-Pb collisions at √ s NN = arXiv:1912.00740 .[5] K. Aamodt, et al., The ALICE experiment at the CERN LHC, JINST 3 (2008) S08002. doi:10.1088/1748-0221/3/08/S08002 .[6] A. Bilandzic, C. H. Christensen, K. Gulbrandsen, A. Hansen, Y. Zhou, Generic framework for anisotropic flow analyses withmultiparticle azimuthal correlations, Phys. Rev. C89 (6) (2014) 064904. arXiv:1312.3572 , doi:10.1103/PhysRevC.89.064904 .[7] P. Staig, E. Shuryak, The Fate of the Initial State Fluctuations in Heavy Ion Collisions. III The Second Act of Hydrodynamics,Phys. Rev. C84 (2011) 044912. arXiv:1105.0676 , doi:10.1103/PhysRevC.84.044912 .[8] R. A. Lacey, Y. Gu, X. Gong, D. Reynolds, N. N. Ajitanand, J. M. Alexander, A. Mwai, A. Taranenko, Is anisotropic flow reallyacoustic? arXiv:1301.0165 .[9] L. Yan, J.-Y. Ollitrault, ν , ν , ν , ν : nonlinear hydrodynamic response versus LHC data, Phys. Lett. B744 (2015) 82–87. arXiv:1502.02502 , doi:10.1016/j.physletb.2015.03.040 .[10] B. B. Abelev, et al., Elliptic flow of identified hadrons in Pb–Pb collisions at √ s NN = .
76 TeV, JHEP 06 (2015) 190. arXiv:1405.4632 , doi:10.1007/JHEP06(2015)190 .[11] S. Acharya, et al., Linear and non-linear flow modes in Pb-Pb collisions at √ s NN = arXiv:1705.04377 , doi:10.1016/j.physletb.2017.07.060doi:10.1016/j.physletb.2017.07.060