Event-by-event multi-harmonic correlations of different flow amplitudes in Pb-Pb collisions at \sqrt{s_{_{\rm NN}}}=2.76 TeV
EEUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-EP-2021-0056 January 2021© 2021 CERN for the benefit of the ALICE Collaboration.Reproduction of this article or parts of it is allowed as specified in the CC-BY-4.0 license.
Event-by-event multi-harmonic correlations of different flow amplitudesin Pb–Pb collisions at √ s NN = . TeV
ALICE Collaboration * Abstract
The genuine event-by-event correlations between three flow amplitudes are measured for the firsttime in Pb–Pb collisions at √ s NN = .
76 TeV by the ALICE Collaboration at the Large HadronCollider. The results are obtained with recently developed observables, the higher order Sym-metric Cumulants (SC), in the midrapidity region | η | < . . < p T < . c . These higher order observables show the same robustness against systematicbiases arising from nonflow effects as the two-harmonic SC. The new results cannot be interpretedin terms of lower order flow measurements, since they are dominated by different patterns of event-by-event flow fluctuations. The results are compared with expectations from initial state modelssuch as T R ENTo and next-to-leading order perturbative-QCD+saturation model of initial conditions,followed by iEBE-VISHNU and EKRT viscous hydrodynamic calculations. Model comparisons pro-vide an indication of the development of genuine correlations between the elliptic v , the triangular v and the quadrangular v flow amplitudes during the collective evolution of the medium. The com-parison with the predictions for the correlations between v , v and the pentagonal flow magnitude v illustrate the need for further tuning of model parameterizations. Therefore, these results can providenew and independent constraints for the initial conditions and system properties of nuclear mattercreated in heavy-ion collisions, complementary to previous flow measurements. * See Appendix A for the list of collaboration members a r X i v : . [ nu c l - e x ] J a n vent-by-event multi-harmonic correlations... ALICE CollaborationUnder extreme values of temperature and/or baryon density, the fundamental theory of the strong nuclearforce, quantum chromodynamics (QCD), predicts the existence of a quark–gluon plasma (QGP). In theQGP state, quarks are deconfined from ordinary hadrons, but contrary to the initial theoretical expecta-tions, they remain strongly coupled with the other liberated quarks and form a liquid state [1]. Resultsextracted from heavy-ion collision data are consistent with the scenario in which the QGP undergoescollective expansion, during which the dominant feature is its hydrodynamic response to the anisotropiesin the initial state geometry. This phenomenon is known as anisotropic flow [2]. The collective dynamicsof the QGP is sensitive to η / s and ζ / s , where η and ζ are shear and bulk viscosities, and s the entropydensity. The overall success of hydrodynamic models to describe the heavy-ion data was pivotal in de-termining that the value of η / s of the QGP is lower than that of any other liquid found in nature [3]. Thisconclusion established the perfect liquid paradigm, which is one of the most striking recent discoveriesin high-energy physics [4–6].In models that describe heavy-ion collisions the produced matter evolves collectively, with particlesbeing emitted independently along the azimuthal direction with a distribution f ( ϕ ) . The Fourier seriesof this distribution is given by f ( ϕ ) = π (cid:34) + ∞ ∑ n = v n cos [ n ( ϕ − Ψ n )] (cid:35) , (1)where the flow amplitude v n and the symmetry plane angle Ψ n are two independent degrees of freedomto quantify anisotropic flow [7]. Experimental challenges of measuring these anisotropic flow observ-ables are overcome with the development of multiparticle azimuthal correlations [8–12]. A great deal ofadditional information can be extracted from correlations between different flow amplitudes or differentsymmetry planes, or from observables which are sensitive to their intercorrelations [13–17].The multiparticle observables which quantify the correlations between event-by-event fluctuations oftwo different flow amplitudes, the Symmetric Cumulants (SC), were studied in Refs. [12, 18]. That ini-tial analysis focused only on the centrality dependence of correlations between lower order amplitudesusing SC ( k , l ) ≡ (cid:104) v k v l (cid:105) − (cid:104) v k (cid:105)(cid:104) v l (cid:105) , where the angular brackets denote an average over all events. It waslater extended to higher orders (up to 5 th order) as well as to the transverse momentum ( p T ) dependenceof correlations for the lower order amplitudes in Ref. [19]. These results revealed that correlations amongdifferent flow magnitudes depend on harmonic orders as well as the collision centrality, while showingmoderate p T dependence in semicentral collisions. It was found that the different SC( k , l ) observableshave different sensitivities to the initial conditions of a heavy-ion collision and the properties of thecreated system, while providing discriminating power in separating the effects of η / s from the initialconditions in the final state particle anisotropies. In addition, the SC observables exhibit a better sen-sitivity to the temperature dependence η / s ( T ) than the individual flow amplitudes, which are sensitiveonly to the average values (cid:104) η / s (cid:105) [18, 20].In this paper, a new set of observables, dubbed higher order SC , are analyzed [21]. These higher orderobservables extract the genuine correlation among multiple flow amplitudes, and provide new and inde-pendent constraints for both the initial conditions and the QGP properties. The genuine correlation (orcumulant) of three flow amplitudes can be obtained with the following expression [21, 22]:SC ( k , l , m ) ≡ (cid:10) v k v l v m (cid:11) − (cid:10) v k v l (cid:11) (cid:10) v m (cid:11) − (cid:10) v k v m (cid:11) (cid:10) v l (cid:11) − (cid:10) v l v m (cid:11) (cid:10) v k (cid:11) + (cid:10) v k (cid:11) (cid:10) v l (cid:11) (cid:10) v m (cid:11) . (2)The observable SC( k , l , m ) is, by definition, the 3rd order cumulant of three flow amplitudes v k , v l and v m .If the previously used low order flow observables, like v n { } , v n { } [10] or SC( k , l ) [12], would be able tocharacterize all collective correlations and anisotropic flow in the system, SC( k , l , m ) would be identicallyzero. On the contrary, the non-vanishing results for SC( k , l , m ) provide access to the information to whichthese traditionally used flow observables are insensitive. A further refinement can be achieved with the2vent-by-event multi-harmonic correlations... ALICE Collaborationnormalized versions of these observables defined asNSC ( k , l , m ) ≡ SC ( k , l , m ) (cid:104) v k (cid:105)(cid:104) v l (cid:105)(cid:104) v m (cid:105) , (3)which makes it easier to identify the origin of the correlations, either from the initial stage or from thecollective expansion [21].Another important aspect is the sign of the SC( k , l , m ) observables which is not trivial and can be under-stood if the definition in Eq. (2) is rewritten as:SC ( k , l , m ) = (cid:10)(cid:0) v k − (cid:10) v k (cid:11)(cid:1) (cid:0) v l − (cid:10) v l (cid:11)(cid:1) (cid:0) v m − (cid:10) v m (cid:11)(cid:1)(cid:11) . (4)For SC ( k , l , m ) > v k > (cid:10) v k (cid:11) and v l > (cid:10) v l (cid:11) , then the probability to find v m > (cid:10) v m (cid:11) in that event is enhanced (this case ismarked as (+ , + , +) pattern in the event-by-event flow fluctuations); b) if v k > (cid:10) v k (cid:11) and v l < (cid:10) v l (cid:11) inan event, that enhances the probability to find v m < (cid:10) v m (cid:11) in that event and this is marked as (+ , − , − ) pattern. By using the same reasoning, it can be concluded that SC ( k , l , m ) < (+ , + , − ) and ( − , − , − ) patterns. These persistent patterns of event-by-event flow fluctuations are invariant withrespect to permutations of amplitudes of flow harmonics in the definition of SC ( k , l , m ) , and they are adirect imprint of genuine three-harmonic correlations.Since the flow amplitudes cannot be measured directly in an experiment, Eq. (2) can be used only intheoretical studies.It was demonstrated in Ref. [21] that SC ( k , l , m ) , as defined in Eq. (2), can be estimated reliably in anexperiment with the following combination of azimuthal correlators:SC ( k , l , m ) = (cid:104)(cid:104) cos [ k ϕ + l ϕ + m ϕ − k ϕ − l ϕ − m ϕ ] (cid:105)(cid:105)− (cid:104)(cid:104) cos [ k ϕ + l ϕ − k ϕ − l ϕ ] (cid:105)(cid:105) (cid:104)(cid:104) cos [ m ( ϕ − ϕ )] (cid:105)(cid:105)− (cid:104)(cid:104) cos [ k ϕ + m ϕ − k ϕ − m ϕ ] (cid:105)(cid:105) (cid:104)(cid:104) cos [ l ( ϕ − ϕ )] (cid:105)(cid:105)− (cid:104)(cid:104) cos [ l ϕ + m ϕ − l ϕ − m ϕ ] (cid:105)(cid:105) (cid:104)(cid:104) cos [ k ( ϕ − ϕ )] (cid:105)(cid:105) + (cid:104)(cid:104) cos [ k ( ϕ − ϕ )] (cid:105)(cid:105) (cid:104)(cid:104) cos [ l ( ϕ − ϕ )] (cid:105)(cid:105) (cid:104)(cid:104) cos [ m ( ϕ − ϕ )] (cid:105)(cid:105) . (5)The double average notation indicates that in the first step averaging is performed over all distinct com-binations of 2, 4, or 6 particles within the same event, and then these results are averaged over all events.Each azimuthal correlator in the above estimator can be measured efficiently and exactly with the GenericFramework published in Ref. [12]. By definition, this estimator ensures that large systematic biases fromself-correlations and symmetry planes Ψ n are eliminated. In the absence of nonflow (correlations be-tween a few particles unrelated to collective phenomena and anisotropic flow), it reduces analytically toEq. (2), even for the case of large event-by-event flow fluctuations [21].The results presented in this paper are obtained with the data sample from Pb–Pb collisions at √ s NN = .
76 TeV collected with the ALICE detector in 2010. After the event and track selection criteria areapplied, the data sample corresponds to about 8 . × minimum bias events for the 0–50% centralityrange.A detailed description of the ALICE detector and its performance can be found in Refs. [23–26]. Thetime projection chamber (TPC) was used to reconstruct charged particles and measure their momentawith full azimuthal coverage in the pseudorapidity range | η | < . . < η < . − . < η < − .
7, respectively, were used for triggering and for an alternative deter-mination of centrality [30–32]. The trigger conditions are identical to those described in Refs. [30, 33].The event and track selection criteria are based on the previous lower order SC analyses [18, 19]. Arequirement that the reconstructed primary vertex (PV) is within ±
10 cm from the nominal interactionpoint along the beam axis is applied. The main analysis is performed using tracks reconstructed onlywith the TPC (referred to as TPC-only further in the text) in the kinematic range 0 . < p T < . c and | η | < .
8. The low p T cutoff decreases the biases from the smaller reconstruction efficiency, whilethe high p T cutoff reduces the anisotropic contaminations in the azimuthal distributions emerging fromthe jets. The selected tracks are reconstructed with a minimum of 70 space points out of the maximum of159 in TPC and the χ / NDF of their momentum fit is required to be 0 . < χ / NDF < .
0. Furthermore,only tracks with a maximum distance of closest approach (DCA) to the primary vertex of 2 . . K ± decays, are rejected. Using the previous selectioncriteria, the contamination from secondaries in TPC-only tracks varies from about 16% at 0 . c to about 7% at 5 GeV/ c . The track reconstruction efficiency is almost constant at about 80–88% as afunction of transverse momentum.Corrections both for non-uniform reconstruction efficiency (NUE) as a function of transverse momentumand non-uniform acceptance (NUA) as a function of azimuthal angle are computed in form of particleweights to each individual azimuthal correlator in Eq. (5), by following the prescription outlined inRef. [12]. Particle weights for NUE were obtained with the Monte Carlo generator HIJING (Heavy-IonJet INteraction Generator) [35], by comparing the p T yields at reconstructed and generated level. On theother hand, particle weights for NUA are data driven, since due to random event-by-event fluctuations ofthe impact parameter vector (which is defined as a vector connecting two centers of colliding heavy-ions),the azimuthal distribution of produced particles averaged over all events must be flat for a detector withuniform azimuthal acceptance. Only corrections for NUE as a function of p T are applied to all the tracksselected for the main analysis using the default selection criteria. Effects of NUA in the distribution ofazimuthal angles of TPC-only tracks were also checked, but found to be negligible.The estimator in Eq. (5) can be systematically biased due to nonflow correlations, which can be estimatedwith HIJING. This is a widely used Monte Carlo model to study particle production and jets in nuclearcollisions that implements all relevant sources of nonflow correlations (jet production and fragmenta-tion, particle decays, etc.), but has no collective effects like anisotropic flow. Therefore, it is an idealrealistic model to estimate the nonflow contribution in the SC( k , l , m ) observables. The overall nonflowcontribution to SC( k , l , m ) exhibits the generic scaling as a function of multiplicity M , which can be pa-rameterized as δ SC3 = α M + β M + γ M , where α , β and γ are three constants [21]. In heavy-ion collisions,characterized by large values of multiplicity, such contribution is well suppressed. For all SC( k , l , m ) ob-servables reported in this paper, HIJING results are compatible with zero for the centrality range 0–50%(for instance, predictions for SC(2,3,4) and SC(2,3,5) can be found in Fig. 7 of Ref. [21]).The remaining systematic uncertainties are estimated by varying each criterion of the event and trackselection independently. The values of SC ( k , l , m ) obtained after the variation are compared in eachcentrality interval with the ones from the default selection. The variation contributes to the systematicuncertainty if the difference between the two results lie more than one σ away from zero. In the previous, σ is the uncertainty of the difference, calculated considering the correlation between the two results. Thetotal systematic uncertainty is obtained as the quadratic sum of all sources. The importance of each trialdepends on the observable under consideration. The data sample was collected with two configurations4vent-by-event multi-harmonic correlations... ALICE Collaborationof the magnetic field polarity in the solenoid magnet in which the ALICE central barrel detectors areembedded, giving two samples with similar numbers of events. As the main analysis uses both samples,the systematic effect is estimated individually for each orientation of the field polarity. No significantimpact is seen in this case. In the next paragraph, the ranges of relative variations observed in semicentralcollisions for each trial are reported. It has to be noted that the variations observed in collisions witha centrality up to 20%, and for SC ( , , ) and SC ( , , ) in the range 20–30%, can be larger thanthe ones indicated due to the small size of the signal and are therefore not reported. The systematicuncertainties are represented by the shaded boxes around each data point in all figures. On the otherhand, there are variations which impact some, if not all, of the analysed combinations of SC( k , l , m ).For example, the distance of the PV to the nominal interaction point along the beam direction whenchanged to ± ±
12 cm does not impact half of the combinations, i.e. SC ( , , ) , NSC ( , , ) and SC ( , , ) , but results to an uncertainty of about 3 .
2% for SC ( , , ) and NSC ( , , ) . For thetightening the DCA criterion in the plane transverse to the beam direction from 2 . ( , , ) is not affected, while there is an effect of about 12% for NSC ( , , ) to about36% for SC ( , , ) . The default analysis uses the centrality estimated from the particle multiplicity inthe SPD, while the systematic check is based on the determination of the centrality with the V0 detector.This change impacts the final results for all combinations with the exception of SC ( , , ) , with valuesranging from about 15% for SC ( , , ) and its normalised version to 21% for SC ( , , ) . The variationof the number of space points in the TPC, from at least 70 points to 50 and then to 100, leads to systematicbias in the final results in SC ( , , ) , SC ( , , ) and NSC ( , , ) ranging from 5% for SC ( , , ) to14% for SC ( , , ) . This is also the case for the quality of fit χ / NDF , when the default range of0 . < χ / NDF < . . < χ / NDF < . . < χ / NDF < .
5. This leads tosignificant differences for SC ( , , ) , SC ( , , ) and NSC ( , , ) (about 12% for NSC ( , , ) ), and forthe tightening of the DCA criterion along the beam axis from 3 . . ( , , ) and itsnormalised version (about 8–10%). Finally, non-negligible systematic effects can be seen using hybridtracks, which also contain smaller contamination from secondaries, leading to an estimation of theirsystematic effects in the default selection. For this last systematic check, all combinations see significantchanges (between 4% and 19% for SC ( , , ) and NSC ( , , ) , respectively).The centrality dependence of SC( k , l , m ) and NSC( k , l , m ) for the different combinations of flow am-plitudes is shown in Fig. 1 (a) and Fig. 1 (b), respectively. When moving from central to semicentralcollisions, the deviation from zero of both SC ( , , ) and SC ( , , ) becomes stronger, albeit with op-posite sign. These non-zero values for semicentral collisions are the first experimental indications ofgenuine correlations between three flow amplitudes. The results for SC ( , , ) provide new and inde-pendent constraints on the non-linear response contribution in v from v and v , which for the first timedo not require any assumption in the derivation on the nature of two-harmonic correlations [36]. For thehigher order flow amplitudes, the measurements for SC ( , , ) and SC ( , , ) are compatible with zerofor all centralities. The negative increasing trend observed for SC ( , , ) is also present for NSC ( , , ) (Fig. 1(b)). However, this is not the case for the pair SC ( , , ) and NSC ( , , ) . The increase seen inthe former cannot be found in the latter, which shows a decrease for semicentral events. This differentbehavior originates from the fact that the non-linear response introduces a genuine correlation among allthree amplitudes in SC(2,3,5), while such contribution is not present in SC(2,3,4). The signatures of allobservables hold for the whole centrality range within uncertainties.The results for the higher order SC observables are compared with the event-by-event Eskola-Kajantie-Ruuskanen-Tuominen (EKRT)+viscous [20] and T R ENTo + iEBE-VISHNU hydrodynamic models [37].In the EKRT model, the initial energy density profiles are calculated using a next-to-leading orderperturbative-QCD+saturation model [38, 39]. The subsequent space–time evolution is described by rel-ativistic dissipative fluid dynamics with different temperature parameterizations η / s ( T ) . This state-of-the-art model gives a good description of the charged hadron multiplicity and the low- p T region of thecharged hadron spectra at BNL’s Relativistic Heavy Ion Collider and at CERN’s Large Hadron Collider5vent-by-event multi-harmonic correlations... ALICE Collaboration ) k , l , m S C ( - - - - - - - - · (a) = 2.76 TeV NN s Pb - ALICE Pb| < 0.8 h | c < 5.0 GeV/ T p Centrality percentile0 10 20 30 40 50 ) k , l , m N S C ( - - (b)NSC(2,3,4)NSC(2,3,5) Figure 1:
Centrality dependence of SC(2,3,4), SC(2,3,5), SC(2,4,6) and SC(3,4,5) (a) and of NSC(2,3,4) andNSC(2,3,5) (b) in Pb–Pb collisions at √ s NN = .
76 TeV. The statistical (systematic) uncertainties are shown withthe lines (boxes). (see Figs. 11–13 in Ref. [20]). Each of the η / s ( T ) parameterizations is adjusted to reproduce the mea-sured v n from central to semiperipheral collisions (see Fig. 15 in Ref. [20] and Fig. A.2 in Ref. [19]).For the “param1” parameterization of η / s ( T ) , the phase transition from the hadronic to the QGP phaseoccurs at the lowest temperature, around 150 MeV [20]. This parameterization is also characterized bya moderate slope in η / s ( T ) which decreases (increases) in the hadronic (QGP) phase. The model calcu-lations in which the temperature of the phase transition is larger than for “param1” parameterization areruled out by the previous measurements [18, 19]. In the study presented in this paper, the EKRT predic-tion for the centrality dependence of SC( k , l , m ) was obtained from a sample consisting of 40k events inthe 0–100% centrality range.The calculations for the η / s ( T ) = “param1” parametrisation, which gives a good description of the lowerorder SC results, are thus compared to our new results for higher order SC in Fig. 2. They can describethe overall trends of all combinations in the centrality dependence. However, SC ( , , ) is found to bestrictly positive in models.The hybrid hydrodynamic model T R ENTo+iEBE-VISHNU has successfully described the previous AL-6vent-by-event multi-harmonic correlations... ALICE Collaboration S C ( , , ) - - - - - - - · (a) -9 x10 ALICEENTo R TEKRT IS = param1 /s h EKRT, ENTo+iEBE-VISHNU, MAP R T Centrality percentile0 10 20 30 40 50 N S C ( , , ) - - - - - - - (b) = 2.76 TeV NN s Pb - ALICE Pb| < 0.8 h | c < 5.0 GeV/ T p S C ( , , ) - - · (c) -9 x10 N S C ( , , ) (d) Centrality percentile 0 10 20 30 40 50 S C ( , , ) - - - - · (e) -12 x10 Centrality percentile0 10 20 30 40 50 S C ( , , ) - - · (f) -12 x10 Figure 2:
Predictions from the hydrodynamical models for the centrality dependence for the SC( k , l , m ) [panels(a), (c), (e) and (f)] and NSC( k , l , m ) [panels (b) and (d)] in Pb–Pb collisions at √ s NN = .
76 TeV. The statisticaluncertainties are shown with coloured bands. The predictions are compared with the ALICE results from Fig. 1shown with red markers.
ICE measurements [37]. It consists of the T R ENTo model [40] for the initial condition, which is con-nected with a free streaming to a 2+1 dimensional causal hydrodynamic model VISH2+1 [41, 42]. Theevolution is continued after particlization via the UrQMD model [43, 44]. The initial conditions, η / s ( T ) , ζ / s ( T ) and other free parameters of the hybrid model are extracted by the global Bayesian analysis. Weperform a model calculation with the best-fit parameter points chosen by maximum a posteriori (MAP)for Pb–Pb collisions at √ s NN = .
76 TeV as they are reported in Ref. [37]. All the kinematic cuts suchas transverse momentum and pseudorapidity intervals are matched with the data reported in this article.In heavy-ion collisions, the main source of anisotropy in the azimuthal distribution in the final stateoriginates from anisotropies in the initial state geometry. The initial state geometry can be described byquantities called eccentricities ε n which are the moments of the initial energy (or entropy) density. For7vent-by-event multi-harmonic correlations... ALICE Collaborationinstance, the values of ε and ε indicate to what extent the initial geometry is elliptical and triangular,respectively. For small values of eccentricities, one can approximate the response of the collective evo-lution to the initial state as a linear relation v n = k n ε n [45, 46]. For n = ,
3, this linear approximation ismore accurate than for higher harmonics where non-linear terms play a non-negligible role [13]. If thehigher order eccentricity cumulants are normalized by their averages (analogous to Eq. (3)), the responsecoefficients k n can cancel between numerator and denominator. Therefore, any difference in the NSCvalues calculated from the eccentricities in the initial state to those obtained from the measured flowamplitudes in the final state is an indication of a hydrodynamic non-linear response.The comparison to the T R ENTo+iEBE-VISHNU calculation is shown in Fig. 2. The overall trends inthe centrality dependence are captured by this model. Both SC(2,3,4) and SC(2,3,5) are clearly under-estimated, while NSC(2,3,4) and NSC(2,3,5) are in a better agreement with the data. In the case ofNSC( k , l , m ), predictions from T R ENTo for the initial state are also shown in Fig. 2. As iEBE-VISHNUuses T R ENTo as input, the comparisons between the two sets of predictions can give insights aboutthe development of correlations in the system. The relative change in NSC(2,3,4) for iEBE-VISHNUcalculations from the ones from T R ENTo for 10–30% centralities indicates that the correlations havedeveloped during the hydrodynamic evolution of the medium. The same phenomenon is hinted withinuncertainties in NSC(2,3,5). In this latter case, this can be explained by the non-linear response contri-bution to v induced by the low order v and v found in Refs. [47, 48]. For SC(2,4,6) and SC(3,4,5),iEBE-VISHNU is in agreement with the predictions from EKRT within uncertainties.Recent Bayesian analyses [37, 49] show that the T R ENTo model reproduces certain features of EKRTmodels with the energy deposition parameter, p ≈ R ENTo model shows stronger correlations than the EKRT model in semicentral collisions and theresulting SC( k , l , m ) show differences as well. Since the EKRT-hydro model does not include effects frombulk viscosity yet and the extracted bulk viscosities from two different Bayesian analyses give sizeabledifferences, more theoretical studies will be necessary to get any firm conclusions. In summary, wehave presented the first measurements of event-by-event correlations between three flow amplitudes, ob-tained with higher order SC observables in Pb–Pb collisions at √ s NN = .
76 TeV. The non-zero valuesof SC ( k , l , m ) for semicentral collisions are the first experimental indication of genuine correlations be-tween three flow amplitudes. The relative changes between T R ENTo and iEBE-VISHNU for NSC(2,3,4)and NSC(2,3,5) are consistent with the development of correlations during the collective evolution ofthe medium. A similar indication can be extracted from the EKRT model. These results provide newconstraints on the non-linear response contribution in v from v and v . The new results for SC ( k , l , m ) provide independent constraints for the initial conditions, system properties, non-linear response andpossible patterns of event-by-event flow fluctuations. Acknowledgements
The ALICE Collaboration would like to thank Harri Niemi for providing the latest predictions from thestate-of-the-art hydrodynamic model.The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable con-tributions to the construction of the experiment and the CERN accelerator teams for the outstandingperformance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources andsupport provided by all Grid centres and the Worldwide LHC Computing Grid (WLCG) collaboration.The ALICE Collaboration acknowledges the following funding agencies for their support in buildingand running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics In-stitute) Foundation (ANSL), State Committee of Science and World Federation of Scientists (WFS),Armenia; Austrian Academy of Sciences, Austrian Science Fund (FWF): [M 2467-N36] and National-stiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High8vent-by-event multi-harmonic correlations... ALICE CollaborationTechnologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de DesenvolvimentoCientífico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo àPesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS),Brazil; Ministry of Education of China (MOEC) , Ministry of Science & Technology of China (MSTC)and National Natural Science Foundation of China (NSFC), China; Ministry of Science and Educationand Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear(CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, CzechRepublic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN andDanish National Research Foundation (DNRF), Denmark; Helsinki Institute of Physics (HIP), Finland;Commissariat à l’Energie Atomique (CEA) and Institut National de Physique Nucléaire et de Physiquedes Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesmin-isterium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für SchwerionenforschungGmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Researchand Religions, Greece; National Research, Development and Innovation Office, Hungary; Departmentof Atomic Energy Government of India (DAE), Department of Science and Technology, Governmentof India (DST), University Grants Commission, Government of India (UGC) and Council of Scientificand Industrial Research (CSIR), India; Indonesian Institute of Science, Indonesia; Istituto Nazionaledi Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology , Nagasaki Instituteof Applied Science (IIST), Japanese Ministry of Education, Culture, Sports, Science and Technology(MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacionalde Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tec-nología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico;Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Coun-cil of Norway, Norway; Commission on Science and Technology for Sustainable Development in theSouth (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Science andHigher Education, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science andTechnology Information and National Research Foundation of Korea (NRF), Republic of Korea; Min-istry of Education and Scientific Research, Institute of Atomic Physics and Ministry of Research andInnovation and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Min-istry of Education and Science of the Russian Federation, National Research Centre Kurchatov Institute,Russian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Educa-tion, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation ofSouth Africa, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Founda-tion (KAW), Sweden; European Organization for Nuclear Research, Switzerland; Suranaree Universityof Technology (SUT), National Science and Technology Development Agency (NSDTA) and Office ofthe Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic EnergyAgency (TAEK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilities Council (STFC), United Kingdom; National Science Foundation of the United States of Amer-ica (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United Statesof America.
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Menchaca-Rocha , C. Mengke , ,E. Meninno , , A.S. Menon , M. Meres , S. Mhlanga , Y. Miake , L. Micheletti ,L.C. Migliorin , D.L. Mihaylov , K. Mikhaylov , , A.N. Mishra , , D. Mi´skowiec ,A. Modak , N. Mohammadi , A.P. Mohanty , B. Mohanty , M. Mohisin Khan , Z. Moravcova ,C. Mordasini , D.A. Moreira De Godoy , L.A.P. Moreno , I. Morozov , A. Morsch ,T. Mrnjavac , V. Muccifora , E. Mudnic , D. Mühlheim , S. Muhuri , J.D. Mulligan ,A. Mulliri , M.G. Munhoz , R.H. Munzer , H. Murakami , S. Murray , L. Musa ,14vent-by-event multi-harmonic correlations... ALICE CollaborationJ. Musinsky , C.J. Myers , J.W. Myrcha , B. Naik , R. Nair , B.K. Nandi , R. Nania ,E. Nappi , M.U. Naru , A.F. Nassirpour , C. Nattrass , S. Nazarenko , A. Neagu , L. Nellen ,S.V. Nesbo , G. Neskovic , D. Nesterov , B.S. Nielsen , S. Nikolaev , S. Nikulin , V. Nikulin ,F. Noferini , S. Noh , P. Nomokonov , J. Norman , N. Novitzky , P. Nowakowski ,A. Nyanin , J. Nystrand , M. Ogino , A. Ohlson , J. Oleniacz , A.C. Oliveira Da Silva ,M.H. Oliver , A. Onnerstad , C. Oppedisano , A. Ortiz Velasquez , T. Osako , A. Oskarsson ,J. Otwinowski , K. Oyama , Y. Pachmayer , S. Padhan , D. Pagano , G. Pai´c ,A. Palasciano , J. Pan , S. Panebianco , P. Pareek , J. Park , J.E. Parkkila , S. Parmar ,S.P. Pathak , B. Paul , J. Pazzini , H. Pei , T. Peitzmann , X. Peng , L.G. Pereira , H. Pereira DaCosta , D. Peresunko , G.M. Perez , S. Perrin , Y. Pestov , V. Petráˇcek , M. Petrovici ,R.P. Pezzi , S. Piano , M. Pikna , P. Pillot , O. Pinazza , , L. Pinsky , C. Pinto , S. Pisano ,M. Płosko´n , M. Planinic , F. Pliquett , M.G. Poghosyan , B. Polichtchouk , N. Poljak ,A. Pop , S. Porteboeuf-Houssais , J. Porter , V. Pozdniakov , S.K. Prasad , R. Preghenella ,F. Prino , C.A. Pruneau , I. Pshenichnov , M. Puccio , S. Qiu , L. Quaglia , R.E. Quishpe ,S. Ragoni , A. Rakotozafindrabe , L. Ramello , F. Rami , S.A.R. Ramirez , A.G.T. Ramos ,R. Raniwala , S. Raniwala , S.S. Räsänen , R. Rath , I. Ravasenga , K.F. Read , ,A.R. Redelbach , K. Redlich V , , A. Rehman , P. Reichelt , F. Reidt , R. Renfordt ,Z. Rescakova , K. Reygers , A. Riabov , V. Riabov , T. Richert , , M. Richter , P. Riedler ,W. Riegler , F. Riggi , C. Ristea , S.P. Rode , M. Rodríguez Cahuantzi , K. Røed , R. Rogalev ,E. Rogochaya , T.S. Rogoschinski , D. Rohr , D. Röhrich , P.F. Rojas , P.S. Rokita ,F. Ronchetti , A. Rosano , , E.D. Rosas , A. Rossi , A. Rotondi , A. Roy , P. Roy ,N. Rubini , O.V. Rueda , R. Rui , B. Rumyantsev , A. Rustamov , E. Ryabinkin , Y. Ryabov ,A. Rybicki , H. Rytkonen , W. Rzesa , O.A.M. Saarimaki , R. Sadek , S. Sadovsky ,J. Saetre , K. Šafaˇrík , S.K. Saha , S. Saha , B. Sahoo , P. Sahoo , R. Sahoo , S. Sahoo ,D. Sahu , P.K. Sahu , J. Saini , S. Sakai , S. Sambyal , V. Samsonov I , , , D. Sarkar ,N. Sarkar , P. Sarma , V.M. Sarti , M.H.P. Sas , , J. Schambach , , H.S. Scheid ,C. Schiaua , R. Schicker , A. Schmah , C. Schmidt , H.R. Schmidt , M.O. Schmidt ,M. Schmidt , N.V. Schmidt , , A.R. Schmier , R. Schotter , J. Schukraft , Y. Schutz ,K. Schwarz , K. Schweda , G. Scioli , E. Scomparin , J.E. Seger , Y. Sekiguchi ,D. Sekihata , I. Selyuzhenkov , , S. Senyukov , J.J. Seo , D. Serebryakov , L. Šerkšnyt˙e ,A. Sevcenco , A. Shabanov , A. Shabetai , R. Shahoyan , W. Shaikh , A. Shangaraev ,A. Sharma , H. Sharma , M. Sharma , N. Sharma , S. Sharma , O. Sheibani ,A.I. Sheikh , K. Shigaki , M. Shimomura , S. Shirinkin , Q. Shou , Y. Sibiriak , S. Siddhanta ,T. Siemiarczuk , T.F.D. Silva , D. Silvermyr , G. Simatovic , G. Simonetti , B. Singh ,R. Singh , R. Singh , R. Singh , V.K. Singh , V. Singhal , T. Sinha , B. Sitar , M. Sitta ,T.B. Skaali , G. Skorodumovs , M. Slupecki , N. Smirnov , R.J.M. Snellings , C. Soncco ,J. Song , A. Songmoolnak , F. Soramel , S. Sorensen , I. Sputowska , J. Stachel , I. Stan ,P.J. Steffanic , S.F. Stiefelmaier , D. Stocco , M.M. Storetvedt , C.P. Stylianidis ,A.A.P. Suaide , T. Sugitate , C. Suire , M. Suljic , R. Sultanov , M. Šumbera , V. Sumberia ,S. Sumowidagdo , S. Swain , A. Szabo , I. Szarka , U. Tabassam , S.F. Taghavi ,G. Taillepied , J. Takahashi , G.J. Tambave , S. Tang , , Z. Tang , M. Tarhini ,M.G. Tarzila , A. Tauro , G. Tejeda Muñoz , A. Telesca , L. Terlizzi , C. Terrevoli ,G. Tersimonov , S. Thakur , D. Thomas , R. Tieulent , A. Tikhonov , A.R. Timmins ,M. Tkacik , A. Toia , N. Topilskaya , M. Toppi , F. Torales-Acosta , S.R. Torres ,A. Trifiró , , S. Tripathy , T. Tripathy , S. Trogolo , G. Trombetta , V. Trubnikov ,W.H. Trzaska , T.P. Trzcinski , B.A. Trzeciak , A. Tumkin , R. Turrisi , T.S. Tveter ,K. Ullaland , E.N. Umaka , A. Uras , M. Urioni , G.L. Usai , M. Vala , N. Valle ,S. Vallero , N. van der Kolk , L.V.R. van Doremalen , M. van Leeuwen , P. Vande Vyvre ,D. Varga , Z. Varga , M. Varga-Kofarago , A. Vargas , M. Vasileiou , A. Vasiliev , O. VázquezDoce , V. Vechernin , E. Vercellin , S. Vergara Limón , L. Vermunt , R. Vértesi ,15vent-by-event multi-harmonic correlations... ALICE CollaborationM. Verweij , L. Vickovic , Z. Vilakazi , O. Villalobos Baillie , G. Vino , A. Vinogradov ,T. Virgili , V. Vislavicius , A. Vodopyanov , B. Volkel , M.A. Völkl , K. Voloshin ,S.A. Voloshin , G. Volpe , B. von Haller , I. Vorobyev , D. Voscek , J. Vrláková ,B. Wagner , M. Weber , A. Wegrzynek , S.C. Wenzel , J.P. Wessels , J. Wiechula , J. Wikne ,G. Wilk , J. Wilkinson , G.A. Willems , E. Willsher , B. Windelband , M. Winn ,W.E. Witt , J.R. Wright , Y. Wu , R. Xu , S. Yalcin , Y. Yamaguchi , K. Yamakawa ,S. Yang , S. Yano , , Z. Yin , H. Yokoyama , I.-K. Yoo , J.H. Yoon , S. Yuan , A. Yuncu ,V. Yurchenko , V. Zaccolo , A. Zaman , C. Zampolli , H.J.C. Zanoli , N. Zardoshti ,A. Zarochentsev , P. Závada , N. Zaviyalov , H. Zbroszczyk , M. Zhalov , S. Zhang ,X. Zhang , Y. Zhang , V. Zherebchevskii , Y. Zhi , D. Zhou , Y. Zhou , J. Zhu , , Y. Zhu ,A. Zichichi , G. Zinovjev , N. Zurlo Affiliation Notes I Deceased II Also at: Italian National Agency for New Technologies, Energy and Sustainable EconomicDevelopment (ENEA), Bologna, Italy
III
Also at: Dipartimento DET del Politecnico di Torino, Turin, Italy IV Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics,Moscow, Russia V Also at: Institute of Theoretical Physics, University of Wroclaw, Poland
Collaboration Institutes A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan,Armenia AGH University of Science and Technology, Cracow, Poland Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, Kiev,Ukraine Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science(CAPSS), Kolkata, India Budker Institute for Nuclear Physics, Novosibirsk, Russia California Polytechnic State University, San Luis Obispo, California, United States Central China Normal University, Wuhan, China Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico Chicago State University, Chicago, Illinois, United States China Institute of Atomic Energy, Beijing, China Chungbuk National University, Cheongju, Republic of Korea Comenius University Bratislava, Faculty of Mathematics, Physics and Informatics, Bratislava,Slovakia COMSATS University Islamabad, Islamabad, Pakistan Creighton University, Omaha, Nebraska, United States Department of Physics, Aligarh Muslim University, Aligarh, India Department of Physics, Pusan National University, Pusan, Republic of Korea Department of Physics, Sejong University, Seoul, Republic of Korea Department of Physics, University of California, Berkeley, California, United States Department of Physics, University of Oslo, Oslo, Norway16vent-by-event multi-harmonic correlations... ALICE Collaboration Department of Physics and Technology, University of Bergen, Bergen, Norway Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy Dipartimento di Fisica e Nucleare e Teorica, Università di Pavia and Sezione INFN, Pavia, Italy Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFNSezione di Torino, Alessandria, Italy Dipartimento di Scienze MIFT, Università di Messina, Messina, Italy Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy European Organization for Nuclear Research (CERN), Geneva, Switzerland Faculty of Electrical Engineering, Mechanical Engineering and Naval Architecture, University ofSplit, Split, Croatia Faculty of Engineering and Science, Western Norway University of Applied Sciences, Bergen,Norway Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague,Prague, Czech Republic Faculty of Science, P.J. Šafárik University, Košice, Slovakia Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt,Germany Fudan University, Shanghai, China Gangneung-Wonju National University, Gangneung, Republic of Korea Gauhati University, Department of Physics, Guwahati, India Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn,Bonn, Germany Helsinki Institute of Physics (HIP), Helsinki, Finland High Energy Physics Group, Universidad Autónoma de Puebla, Puebla, Mexico Hiroshima University, Hiroshima, Japan Hochschule Worms, Zentrum für Technologietransfer und Telekommunikation (ZTT), Worms,Germany Horia Hulubei National Institute of Physics and Nuclear Engineering, Bucharest, Romania Indian Institute of Technology Bombay (IIT), Mumbai, India Indian Institute of Technology Indore, Indore, India Indonesian Institute of Sciences, Jakarta, Indonesia INFN, Laboratori Nazionali di Frascati, Frascati, Italy INFN, Sezione di Bari, Bari, Italy INFN, Sezione di Bologna, Bologna, Italy INFN, Sezione di Cagliari, Cagliari, Italy INFN, Sezione di Catania, Catania, Italy INFN, Sezione di Padova, Padova, Italy INFN, Sezione di Roma, Rome, Italy INFN, Sezione di Torino, Turin, Italy INFN, Sezione di Trieste, Trieste, Italy Inha University, Incheon, Republic of Korea Institute for Gravitational and Subatomic Physics (GRASP), Utrecht University/Nikhef, Utrecht,17vent-by-event multi-harmonic correlations... ALICE CollaborationNetherlands Institute for Nuclear Research, Academy of Sciences, Moscow, Russia Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia Institute of Physics, Homi Bhabha National Institute, Bhubaneswar, India Institute of Physics of the Czech Academy of Sciences, Prague, Czech Republic Institute of Space Science (ISS), Bucharest, Romania Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico iThemba LABS, National Research Foundation, Somerset West, South Africa Jeonbuk National University, Jeonju, Republic of Korea Johann-Wolfgang-Goethe Universität Frankfurt Institut für Informatik, Fachbereich Informatik undMathematik, Frankfurt, Germany Joint Institute for Nuclear Research (JINR), Dubna, Russia Korea Institute of Science and Technology Information, Daejeon, Republic of Korea KTO Karatay University, Konya, Turkey Laboratoire de Physique des 2 Infinis, Irène Joliot-Curie, Orsay, France Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3,Grenoble, France Lawrence Berkeley National Laboratory, Berkeley, California, United States Lund University Department of Physics, Division of Particle Physics, Lund, Sweden Moscow Institute for Physics and Technology, Moscow, Russia Nagasaki Institute of Applied Science, Nagasaki, Japan Nara Women’s University (NWU), Nara, Japan National and Kapodistrian University of Athens, School of Science, Department of Physics , Athens,Greece National Centre for Nuclear Research, Warsaw, Poland National Institute of Science Education and Research, Homi Bhabha National Institute, Jatni, India National Nuclear Research Center, Baku, Azerbaijan National Research Centre Kurchatov Institute, Moscow, Russia Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark Nikhef, National institute for subatomic physics, Amsterdam, Netherlands NRC Kurchatov Institute IHEP, Protvino, Russia NRC «Kurchatov»Institute - ITEP, Moscow, Russia NRNU Moscow Engineering Physics Institute, Moscow, Russia Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom Nuclear Physics Institute of the Czech Academy of Sciences, ˇRež u Prahy, Czech Republic Oak Ridge National Laboratory, Oak Ridge, Tennessee, United States Ohio State University, Columbus, Ohio, United States
Petersburg Nuclear Physics Institute, Gatchina, Russia
Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia
Physics Department, Panjab University, Chandigarh, India
Physics Department, University of Jammu, Jammu, India
Physics Department, University of Rajasthan, Jaipur, India
Physikalisches Institut, Eberhard-Karls-Universität Tübingen, Tübingen, Germany
Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany
Physik Department, Technische Universität München, Munich, Germany
Politecnico di Bari and Sezione INFN, Bari, Italy
Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für18vent-by-event multi-harmonic correlations... ALICE CollaborationSchwerionenforschung GmbH, Darmstadt, Germany
Rudjer Boškovi´c Institute, Zagreb, Croatia
Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
Saha Institute of Nuclear Physics, Homi Bhabha National Institute, Kolkata, India
School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru
St. Petersburg State University, St. Petersburg, Russia
Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria
SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France
Suranaree University of Technology, Nakhon Ratchasima, Thailand
Technical University of Košice, Košice, Slovakia
The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow,Poland
The University of Texas at Austin, Austin, Texas, United States
Universidad Autónoma de Sinaloa, Culiacán, Mexico
Universidade de São Paulo (USP), São Paulo, Brazil
Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
Universidade Federal do ABC, Santo Andre, Brazil
University of Cape Town, Cape Town, South Africa
University of Houston, Houston, Texas, United States
University of Jyväskylä, Jyväskylä, Finland
University of Liverpool, Liverpool, United Kingdom
University of Science and Technology of China, Hefei, China
University of South-Eastern Norway, Tonsberg, Norway
University of Tennessee, Knoxville, Tennessee, United States
University of the Witwatersrand, Johannesburg, South Africa
University of Tokyo, Tokyo, Japan
University of Tsukuba, Tsukuba, Japan
Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France
Université de Lyon, CNRS/IN2P3, Institut de Physique des 2 Infinis de Lyon , Lyon, France
Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France
Université Paris-Saclay Centre d’Etudes de Saclay (CEA), IRFU, Départment de PhysiqueNucléaire (DPhN), Saclay, France
Università degli Studi di Foggia, Foggia, Italy
Università di Brescia and Sezione INFN, Brescia, Italy
Variable Energy Cyclotron Centre, Homi Bhabha National Institute, Kolkata, India
Warsaw University of Technology, Warsaw, Poland
Wayne State University, Detroit, Michigan, United States
Westfälische Wilhelms-Universität Münster, Institut für Kernphysik, Münster, Germany
Wigner Research Centre for Physics, Budapest, Hungary
Yale University, New Haven, Connecticut, United States148