Measurements of mixed harmonic cumulants in Pb-Pb collisions at \mathbf{\sqrt{{\textit s}_{\rm NN}}}=5.02 TeV
aa r X i v : . [ nu c l - e x ] F e b EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-EP-2021-03119 February 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.
Measurements of mixed harmonic cumulants in Pb–Pb collisions at √ s NN = . TeV
ALICE Collaboration * Abstract
Correlations between moments of different flow coefficients are measured in Pb–Pb collisions at √ s NN = .
02 TeV recorded with the ALICE detector. These new measurements are based on mul-tiparticle mixed harmonic cumulants calculated using charged particles in the pseudorapidity region | η | < . . < p T < . c . The centrality dependenceof correlations between two flow coefficients as well as the correlations between three flow coeffi-cients, both in terms of their second moments, are shown. In addition, a collection of mixed harmoniccumulants involving higher moments of v and v is measured for the first time, where the charac-teristic signature of negative, positive and negative signs of four-, six- and eight-particle cumulantsare observed, respectively. The measurements are compared to the hydrodynamic calculations us-ing iEBE-VISHNU with AMPT and TRENTo initial conditions. It is shown that the measurementscarried out using the LHC Run 2 data in 2015 have the precision to explore the details of initial-state fluctuations and probe the nonlinear hydrodynamic response of v and v to their correspondinginitial anisotropy coefficients ε and ε . These new studies on correlations between three flow coef-ficients as well as correlations between higher moments of two different flow coefficients will pavethe way to tighten constraints on initial-state models and help to extract precise information on thedynamic evolution of the hot and dense matter created in heavy-ion collisions at the LHC. * See Appendix A for the list of collaboration members ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration
One of the fundamental questions in the phenomenology of quantum chromodynamics is what are theproperties of matter at extreme densities and temperatures where quarks and gluons are in a state ofmatter called the quark–gluon plasma (QGP) [1, 2]. High-energy heavy-ion collisions at the RelativisticHeavy Ion Collider (RHIC) at BNL and the Large Hadron Collider (LHC) at CERN create such a stateof strongly interacting matter allowing us to study its properties in the laboratory. Anisotropic flow is akey phenomenon that provides important information about the transport properties of the created QGPmatter. Due to large pressure gradients, the anisotropy of the overlapping region between two collidingnuclei causes an anisotropic distribution of the emitted particles in the final state. This anisotropic particledistribution can be quantified by anisotropic flow [3, 4] which is characterized by the single-particleazimuthal distribution, P ( ϕ ) = π " + ∞ ∑ n = v n cos n ( ϕ − Ψ n ) . (1)Here ϕ is the azimuthal angle of the emitted particle, v n and Ψ n are the n -th order flow coefficient andflow symmetry plane, respectively. Both v n and Ψ n define the n -th order flow-vector as −→ V n = v n e in Ψ n .The size and direction of −→ V n related to the initial anisotropy −→ ε n vector is defined by the moments of theshape of the transverse positions of the participating nucleons, −→ ε n = ε n e − in Φ n = − (cid:10) r n e − in φ (cid:11) h r n i , ( n > ) (2)where ε n and Φ n are the magnitude and orientation of −→ ε n , respectively, and h i stands for the average overall participating nucleons in the initial state. For lower orders, n = v n to ε n was expected, with v n = κ n ε n [5, 6] where κ n is a parameter that encodes the transport propertiesof the produced QGP. Later on, it was noticed in models that, already in semi-peripheral collisions, thecorrelation between the initial ε ( ε ) and the final-state v ( v ) is not completely linear, with a non-negligible spread in the correlation between v n and ε n [7]. Such a nonlinear response of lower-order v n should be related to the dynamic evolution of the system, but it was briefly investigated in previousstudies [7–9]. For the higher orders, n ≥ −→ V n receives a significant nonlinear hydrodynamic responsefrom −→ ε , in non-central collisions, which was studied in great detail [10–17].One can describe the distribution of final-state anisotropies using a joint probability density function( p . d . f . ) in terms of v n and Ψ n as P ( v m , v n , ..., Ψ m , Ψ n , ... ) . This is sensitive to the spatial anisotropy ε n , itsevent-by-event fluctuations, the correlations between different orders of anisotropy coefficients and initialparticipant planes Φ n carried by P ( ε m , ε n , ..., Φ m , Φ n , ... ) and it also reflects the early state dynamics andthe transport properties of the QGP. Although ideally one would like to measure P ( v m , v n , ..., Ψ m , Ψ n , ... ) ,this is not straightforward to achieve in experiments, but what can be measured are the projections of thefull p . d . f . on a finite number of variables [18]. Most of these projected distributions could be classifiedinto the following types: (1) v n fluctuations P ( v n ) for both integrated and differential v n measurements,(2) Ψ n fluctuations P ( Ψ n ) in different phase space, (3) correlations involving only flow coefficients P ( v m , v n , ... ) , (4) correlations involving only flow symmetry planes P ( Ψ m , Ψ n , .. ) and (5) mixed correla-tions carrying both flow coefficients and flow symmetry planes.The v n coefficients were measured up to the ninth order with an unprecedented degree of precision [16].The full p . d . f . of single v n coefficients P ( v n ) was either measured with a Bayesian unfolding proce-dure [19, 20] (for n =
2, 3 and 4) or constructed via the measured moments (for n =
2) [21]. It wasfound that the P ( v n ) distribution, which originates from the p.d.f. of initial-state ε n distribution P ( ε n ) ,is described better by an elliptic-power function than a Bessel-Gaussian function [21]. It was also real-ized that during the expansion the produced particles might not share a common flow symmetry planeat different transverse momenta, p T , and pseudorapidity, η [22, 23]. These transverse momentum and2ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaborationpseudorapidity dependent flow vectors fluctuate event-by-event, which also breaks the factorization oftwo-particle correlations V ( p t T , p a T ) into the product of flow coefficients v n ( p t T ) · v n ( p a T ) [24–26]. Suchphenomena were predicted by hydrodynamic calculations and are found to be sensitive to the initial-state density fluctuations and/or to the specific shear viscosity of the expanding medium [22, 23, 27].In addition, analyses of correlations between different order flow vectors [13, 28, 29] show promise toshed additional light on the initial-state conditions. The correlations between different order symmetryplanes were initially investigated in the observable v n / Ψ n [30–33]. This was followed by measurementsof nonlinear flow modes of higher harmonics by ALICE [14–16, 33] as well as event-plane correlationsby ATLAS [28].The correlation observables involving only anisotropic flow coefficients v m and v n were at first measuredwith event-shape engineering studies [13] proceeded by investigations using symmetric cumulants [34],defined as SC ( m , n ) = (cid:10) v n v m (cid:11) − (cid:10) v n (cid:11) (cid:10) v m (cid:11) . To study such correlations without the dependence on in-dividual flow coefficients, the normalized symmetric cumulant NSC ( m , n ) was further proposed [29].It was found that NSC ( , ) , which studies the correlations between v and v , is very sensitive to theinitial conditions and can be used as a good tool to probe initial state ε and ε correlations. On theother hand, NSC ( , ) and also NSC involving higher order flow coefficients, are sensitive to both initialconditions and the QGP properties. Thus, these
NSC measurements have the potential to distinguishbetween various models of QGP evolution in hydrodynamic and transport models [9, 34–37].It is evident that the study of correlations between various moments of different flow coefficients willdeepen our knowledge of the joint p . d . f . for flow magnitudes and angles. However, only correlationsinvolving the second moments of two flow coefficients, v n and v m , have been measured utilizing SC ( m , n ) while the rest have not yet been explored in experiments. In this Letter, an additional step has been madein this direction by using mixed harmonic cumulants ( MHC ) [38] to investigate correlations involvingmore than two different flow coefficients and to study the relationship between higher moments of differ-ent flow coefficients in heavy-ion collisions at the LHC. These new measurements establish a milestonefor the study of the underlying p.d.f. from P ( v n ) to P ( v n , v m ... ) , and significantly improve the overallunderstanding of the initial conditions and the transport properties of the created QGP at the LHC. The multiparticle cumulant of mixed harmonics that involves only flow coefficients, named
MHC , wasintroduced in Ref. [38]. It is defined as an m -observable cumulant [39] in terms of azimuthal angles. Byconstruction, lower order correlations have been subtracted to form genuine multiparticle correlations.Thus, MHC is expected to be insensitive to non-flow effects. This was confirmed in the study of
MHC using the HIJING model [40], which does not generate collective flow phenomena [38]. For
MHC involving only two flow coefficients of second-order, it is identical with the previously defined four-particle symmetric cumulants, i.e.
MHC ( v m , v n ) = SC ( m , n ) . The six-particle cumulant MHC involving v and v is MHC ( v , v ) = hh cos ( ϕ + ϕ + ϕ − ϕ − ϕ − ϕ ) ii− hh cos ( ϕ + ϕ − ϕ − ϕ ) ii hh cos ( ϕ − ϕ ) ii− hh cos ( ϕ + ϕ − ϕ − ϕ ) ii hh cos ( ϕ − ϕ ) ii + hh cos ( ϕ − ϕ ) ii hh cos ( ϕ − ϕ ) ii . (3)Here the double angular brackets indicate the averaging procedure performed first over all possible com-binations of m -particle tuples that form the m -particle correlation and subsequently the weighted averageof all events is calculated with the number of combinations used as an event weight [41]. In the aboveexpressions, lower order (i.e. two- and four-particle) correlations were removed from the six-particlecorrelation, which results in a genuine six-particle correlation between v and v . One can rewrite the3ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaborationexpression in terms of flow coefficients v and v , MHC ( v , v ) = (cid:10) v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) . (4)Likewise, one can define other six-particle mixed harmonic cumulants that contain v and v or v , v and v , in terms of flow coefficients, MHC ( v , v ) = (cid:10) v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) , (5) MHC ( v , v , v ) = (cid:10) v v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) (cid:10) v (cid:11) . (6)Note in general MHC ( v m , v n , v p ) is different from the so-called higher order symmetric cumulant SC ( m , n , k ) proposed in [42]. However, MHC ( v , v , v ) happens to be the same as SC ( , , ) .Similarly, the eight-particle mixed harmonic cumulant is defined as an eight-observable cumulant, whichcan be written in terms of flow coefficients, MHC ( v , v ) = (cid:10) v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v v (cid:11) , (7) MHC ( v , v ) = (cid:10) v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) − (cid:10) v v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) (cid:10) v v (cid:11) , (8) MHC ( v , v ) = (cid:10) v v (cid:11) − (cid:10) v v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) − (cid:10) v (cid:11) (cid:10) v v (cid:11) − (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v (cid:11) (cid:10) v (cid:11) + (cid:10) v (cid:11) (cid:10) v v (cid:11) . (9)To study genuine multiparticle correlations that are independent of the magnitude of the flow coeffi-cients, the normalized mixed harmonic cumulants nMHC involving two flow coefficients v m and v n areconstructed according to: nMHC ( v km , v ln ) = MHC ( v km , v ln ) h v km i h v ln i , ( m k = n l ) . (10)Here nMHC ( v km , v ln ) is independent of the magnitudes of v m and v n and can therefore be used to quan-titatively compare genuine correlations between v km and v ln determined from experimental data to thosedetermined from the model calculations.Analogously, for MHC involving three flow coefficients, we define the corresponding nMHC , nMHC ( v km , v ln , v qp ) = MHC ( v km , v ln , v qp ) h v km i h v ln i (cid:10) v qp (cid:11) , ( m k + n l = p q ) . (11)Since systematic studies of v n coefficients were carried out for n = − v n coefficients themselves.In general, one should be able to construct arbitrary mixed harmonic cumulants to any order. However,due to the limited amount of data available, mixed harmonic cumulants higher than the eighth orderwill not be examined here. All of the previously mentioned v km or v ln are based on two- or multiparticleazimuthal correlations. These can be measured by using the latest development of the generic algorithmfor multiparticle azimuthal correlations [38]. 4ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration This analysis uses data sample from Pb–Pb collisions at √ s NN = . < η < . − . < η < − .
7, respectively [45]. Only eventswith a reconstructed primary vertex within ±
10 cm from the nominal interaction point along the beamdirection were used in this analysis. Removal of background events from, e.g., beam interactions withthe residual gas molecules in the beam pipe and pileup events was performed based on the informationfrom the Silicon Pixel Detector (SPD) and the V0 detector. A sample of 55 × Pb–Pb collisions,which passed these event selection criteria, were used for the analysis.Charged tracks were reconstructed using the Inner Tracking System (ITS) [46] and the Time ProjectionChamber (TPC) [47]. The selected tracks are required to have at least 70 TPC space points (out of amaximum of 159), and the average χ per degree of freedom of the track fit to the TPC space points isrequired to be lower than two. Additionally, a minimum of two hits are required in the ITS to improve themomentum resolution. A selection requiring the pseudorapidity to be within | η | < . p T < . c or p T > . c were rejected due to the magneticfield and to reduce the contribution from jets, respectively [48]. In addition, a criterion on the maximumdistance of closest approach of the track to the collision point of less than 2 cm in the longitudinaldirection and less than a p T -dependent selection in the transverse direction, ranging from 0 . p T = . c to 0 .
016 cm at p T = . c , was applied. This results in a residual contaminationfrom secondary particles from weak decays and from interactions in the detector material of 1–3%, whichis negligible in the final systematic uncertainty. These selection criteria result in a transverse momentumdependent efficiency of track reconstruction of about 80%.Numerous potential sources of systematic uncertainty were investigated in the analysis, including vari-ations of the event and track selection and the uncertainty associated with possible remaining non-floweffects. These are the azimuthal angle correlations not associated with the common symmetry planes,including contributions from jets and resonance decays, and are found to be negligible for all of the pre-sented observables. The variation of the results with the choice of collision centrality was calculated byalternatively using the SPD to estimate the event multiplicity and was found to contribute less than 5%for all observables. Results with opposite polarities of the magnetic field within the ALICE detector andwith narrowing the nominal ±
10 cm range of the reconstructed vertex along the beam direction fromthe center of the ALICE detector to 9, 8, and 7 cm showed a difference of 0–5.4% compared to resultswith the default selection criteria. The contribution from pileup events was investigated by varying theselections on the correlations between multiplicities from the V0 and SPD, and was found to be negli-gible. The sensitivity to the track selection criteria was explored by varying the number of TPC spacepoints and by comparing the results to those obtained with tracks with different requirements on hitsin the ITS. The effect of varying the number of TPC space points from 70 to 80 and 90 resulted in anegligible systematic uncertainty. Using different track requirements led to a difference with respect tothe default selection criteria of less than 4.3% except for nMHC ( v , v , v ) where it was about 16%. Thesystematic uncertainty evaluated for each above-mentioned source found to be statistically significantaccording to the recommendation in [49] were added in quadrature to obtain the measurements’ totalsystematic uncertainty. The centrality dependence of mixed harmonic cumulants with two and three flow coefficients are mea-sured in Pb–Pb collisions at √ s NN = .
02 TeV. The results of nMHC ( v , v ) , nMHC ( v , v ) , nMHC ( v , v ) ,and nMHC ( v , v , v ) are presented in Fig. 1 by blue solid circles, red solid squares, magenta solid stars5ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration Centrality percentile − n M HC ALICE| < 0.8 η , | c < 5.0 GeV/ T p v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC ) v , v , v ( nMHC Pb-Pb 2.76 TeV ) v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC Figure 1:
Centrality dependence of nMHC ( v , v ) , nMHC ( v , v ) , nMHC ( v , v ) and nMHC ( v , v , v ) in Pb–Pbcollisions at √ s NN = .
02 TeV, shown by the solid markers. The statistical (systematic) errors are shown withvertical bars (filled boxes). Comparisons to the previous measurements at 2.76 TeV from Refs. [29, 50], shown bythe open markers, are also presented. Data points are shifted for visibility. and green diamonds, respectively. Positive values of nMHC ( v , v ) and negative values of nMHC ( v , v ) are observed for all centralities, which means that v and v are correlated while v and v are anti-correlated. This indicates that finding v larger than h v i in an event enhances the probability of finding v larger than h v i and v smaller than h v i in that event. For nMHC ( v , v ) , a similar centrality de-pendence as for nMHC ( v , v ) is seen for centralities above 20–30% where the nonlinear hydrodynamicresponse of −→ V plays a significant role [14, 16]. These new measurements are compared in Fig. 1 to thepreviously published results at √ s NN = .
76 TeV, which were named SC ( m , n ) in Ref. [29, 50], shownwith open markers. The results of nMHC ( v , v ) , nMHC ( v , v ) are compatible within uncertainties atthe two different energies, which indicates a weak dependence on the collision energy of these two ob-servables. However, there are differences for nMHC ( v , v ) between the two studied energies, whichincrease towards central collisions. In particular, the measurement at 5.02 TeV changes sign from neg-ative to positive in central collisions, while it remains negative at the lower energy. A similar study ofmultiparticle cumulants in the most central collisions was investigated in great detail in Ref. [51], wherea significant effect from centrality fluctuations was found in Pb–Pb collisions at 5.02 TeV. Moreover, theamplitude of the centrality fluctuations depends on how the centrality was determined.Besides the measurements of correlations between two flow coefficients, the new measurement of cor-relations between three flow coefficients, nMHC ( v , v , v ) , is shown with green diamonds in Fig. 1. Asintroduced above, nMHC ( v , v , v ) is identical to SC ( , , ) , which has been recently measured at alower energy [52]. By construction, the lower order few-particle correlations have been subtracted fromthe higher order correlations in the nMHC . Thus, it is expected that nMHC ( v , v , v ) should be consis-tent with zero, if the correlations between three flow coefficients are purely driven by the correlationsbetween two flow coefficients. It is seen in Fig. 1 that the result of nMHC ( v , v , v ) is located betweenthe nMHC ( v , v ) , nMHC ( v , v ) and nMHC ( v , v ) for the centrality classes under study. More specif-ically, it is positive and closer to nMHC ( v , v ) and nMHC ( v , v ) in the most central collisions, then itchanges sign to negative and shows a similar centrality dependence to nMHC ( v , v ) and nMHC ( v , v ) in non-central collisions. The non-zero result of nMHC ( v , v , v ) for the presented centrality range6ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaborationshows the existence of genuine correlations between three flow coefficients and thus brings new in-formation toward determining P ( v n , v m , ... ) that cannot be obtained from measurements of correlationsbetween two flow coefficients. − − ) v , v ( n M HC ALICE Pb-Pb5.02 TeV2.76 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC H y d r o / D a t a ) v , v ( n M HC ALICE Pb-Pb5.02 TeV2.76 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC H y d r o / D a t a Figure 2:
Centrality dependence of nMHC ( v , v ) and nMHC ( v , v ) in Pb–Pb collisions at √ s NN = .
02 TeV(solid markers) and 2.76 TeV (open markers). Statistical uncertainties are shown as vertical bars and systematicuncertainties as filled boxes. The iEBE-VISHNU calculations [53] for Pb–Pb collisions at 5.02 TeV with TRENToinitial conditions (red shadowed bands) and AMPT initial conditions (blue shadowed bands) are presented, togetherwith the corresponding initial state calculations nMHC ( ε , ε ) , nMHC ( ε , ε ) from the TRENTo (red dot-dashlines) and AMPT model (blue long-dash lines). The same marker (line) styles and colors are used in later figures.Data points are shifted for visibility. In order to gain more information on the initial conditions and transport properties of the created QGPat the LHC, the results are compared with those from hydrodynamic model calculations. Results fromthe hybrid iEBE-VISHNU model with TRENTo initial conditions with specific shear viscosity η / s ( T ) and bulk viscosity ζ / s ( T ) extracted from the best fit of a Bayesian analysis [54] as well as calculationswith AMPT-initial conditions with η / s = .
08 and no bulk viscosity [53] are compared to the data. Bothcalculations can quantitatively describe the flow coefficients from inclusive and identified hadrons [53,55] and also provide a reasonable description of more complicated flow observables, e.g., nonlinearmodes of higher-order flow [15, 16]. Besides these two calculations, the iEBE-VISHNU model withAMPT-initial conditions with η / s = .
20 and no bulk viscosity is also used. This model does not describethe particle spectra nor the flow coefficients and thus should not be compared with the experimental data.In the remaining text, the hydrodynamic calculations using AMPT initial conditions and η / s = .
08 willbe refereed to as "AMPT calculations". However, the comparison of hydrodynamic calculation fromthe same initial state model but with different η / s values can be very useful to study the sensitivity ofvarious nMHC to the η / s of the QGP.Comparisons of the measured nMHC ( v , v ) and nMHC ( v , v ) to hydrodynamic calculations are shownin Fig. 2. In general, the hydrodynamic calculations with both AMPT and TRENTo initial conditions,shown as blue and red shadowed bands, respectively, predict qualitatively the centrality dependence of nMHC . In addition, as v and v are linearly correlated with the initial ε and ε in central and semi-central collisions, compatible results of the final-state nMHC ( v , v ) calculations and the nMHC ( ε , ε ) calculations from the initial-state models are expected [38]. This is indeed shown by the shaded areas and7ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration − ) , v n M HC ( v ALICE Pb-Pb5.02 TeV2.76 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC H y d r o / D a t a − ) v , v , v ( n M HC ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC H y d r o / D a t a Figure 3:
Centrality dependence of nMHC ( v , v ) and nMHC ( v , v , v ) in Pb–Pb collisions at √ s NN = .
02 TeV(solid markers) and 2.76 TeV (open markers). Statistical uncertainties are shown as vertical bars and systematicuncertainties as filled boxes. Data points are shifted for visibility. the dashed lines in Fig. 2 (left). In the same figure, there is also no difference between the calculationsusing AMPT-initial conditions with different η / s values. This suggests that for the presented centralityranges, v ( v ) is linearly correlated with the initial ε ( ε ). Thus, the nMHC ( v , v ) measurements shownin Fig. 2 (left) can be used to directly constrain the correlations between the initial anisotropy coefficients ε and ε without much consideration of the exact value of the transport coefficients in the hydrodynamicmodels. For nMHC ( v , v ) results shown in Fig. 2 (right), both calculations underestimate the data; theTRENTo calculation fits the data better in central collisions, while the AMPT calculation works slightlybetter for centralities above 20%. The initial-state calculations of nMHC ( ε , ε ) are significantly lowerthan the final-state nMHC ( v , v ) calculations, which suggests that the correlation between v and v isnot driven solely by the initial correlation between ε and ε , but it is mainly developed at later stages ofthe system’s dynamic evolution, especially the nonlinear response contribution to v .Figure 3 (left) compares hydrodynamic calculations with the nMHC ( v , v ) measurement. In general,both models generate the same trend of centrality dependence as is seen in data. Notably, the AMPTcalculations also predict the sign change in central collisions, while the TRENTo calculations remainnegative for the entire centrality range. It has also been seen in Ref. [53] that the AMPT calculations al-ways predict a positive correlation in the most central collisions at 2.76 and 5.02 TeV, while the TRENTocalculations are always negative at both collision energies. Although the hydrodynamic calculations of nMHC ( v , v ) from AMPT and TRENTo initial conditions are almost compatible for non-central colli-sions, the initial correlations between ε and ε , quantified by nMHC ( ε , ε ) , are utterly different fromthe two initial-state models, and are far away from the final-state nMHC ( v , v ) calculations. It couldbe attributed to a significant nonlinear hydrodynamic response in v from ε . This nonlinear contribu-tion is strongly anti-correlated with ε and plays a dominant role in the final nMHC ( v , v ) results fornon-central collisions. On the other hand, in the same centrality region, the linear response of v to ε is rather weak [14], and the contributions from correlations between the initial ε and ε in the final nMHC ( v , v ) appear to be minor.To extend the discussion from correlations of two flow coefficients to three flow coefficients, the mea-8ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaborationsurement of nMHC ( v , v , v ) and its comparison to hydrodynamic calculations with both AMPT andTRENTo initial conditions are presented in Fig. 3 (right). In general, the agreement between the ini-tial nMHC ( ε , ε , ε ) correlations and the final-state nMHC ( v , v , v ) calculations worsens as the col-lision centrality becomes more peripheral, which can be expected due to the increasing contributionfrom the nonlinear hydrodynamic response in v . Figure 3 (right) also shows clearly that the calcula-tion with AMPT initial conditions and η / s = .
08 describes the data reasonably well. The calculationwith η / s = .
20 is two times larger than the one with η / s = .
08. Such a difference is more signif-icant compared to what has been seen in the correlations between two harmonics, where no obviousdifference is observed for nMHC ( v , v ) and nMHC ( v , v ) and only a relatively small difference isseen for nMHC ( v , v ) . This demonstrates the novelty of the new correlations between three flow co-efficients constraining the transport properties of the QGP. However, despite the fact that the hydrody-namic calculations using TRENTo initial conditions are consistent with the measured nMHC ( v , v ) and nMHC ( v , v ) , and also provide a reasonable description of the nMHC ( v , v ) measurement, they signif-icantly underestimate the data by roughly a factor of two. Considering an apparent discrepancy betweenthe data and TRENTo calculations, there is little doubt that the hydrodynamic framework and its corre-sponding parameters can be better tuned in a future Bayesian analysis if this new nMHC ( v , v , v ) mea-surement is used as an input. The first measurement of correlations between three harmonics providesadditional independent constraints on the theoretical models beyond those provided by the correlationsof two harmonics that have been studied before. Centrality percentile − − − − − ) l v , k v ( n M HC ) v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC ) v , v ( nMHC | < 0.8 η , | c < 5.0 GeV/ T p Figure 4:
Centrality dependence of nMHC for Pb–Pb collisions at √ s NN = .
02 TeV. Statistical uncertainties areshown as vertical bars and systematic uncertainties as filled boxes. Data points are shifted for visibility.
With the recently proposed observable nMHC , one can study not only the correlations between two orthree different flow coefficients, in terms of their second moments, but also the correlations between the k th order moment of v m and the l th order moment of v n where k ≥ l ≥
2. It is particularly interestingto study the correlations between various moments of v and v because in central and semi-centralcollisions, both v and v are linearly correlated to their corresponding initial eccentricities ε and ε [8,9]. Thus the measurement of nMHC ( v k , v l ) in central and semi-central collisions might provide a directconstraint on the initial correlation between (cid:10) ε k (cid:11) and (cid:10) ε l (cid:11) . This information is extremely important forthe understanding of the initial conditions of heavy-ion collisions but it has never been measured before.Conversely, the potential nonlinearity of v and v , more pronounced in peripheral collisions, stronglydepends on the dynamical evolution of the created QGP. The study of nMHC ( v k , v l ) will enable a new9ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaborationway to study this effect on v and v . ) , v n M HC ( v ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC
Centrality percentile12 H y d r o / D a t a ) , v n M HC ( v ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC
Centrality percentile024 H y d r o / D a t a Figure 5:
Centrality dependence of nMHC ( v , v ) and nMHC ( v , v ) in Pb–Pb collision at √ s NN = .
02 TeV.Statistical uncertainties are shown as vertical bars and systematic uncertainties as filled boxes.
The first measurements of nMHC ( v k , v l ) are presented in Fig. 4. In addition to the negative value of nMHC ( v , v ) , which has been studied before, positive correlations are observed for both six-particlemixed harmonic cumulants nMHC ( v , v ) and nMHC ( v , v ) . The eight-particle mixed harmonic cu-mulants nMHC ( v , v ) , nMHC ( v , v ) and nMHC ( v , v ) are all negative. Such characteristic negative,positive and negative signs of four-, six-, and eight-particle mixed harmonic cumulants, respectively, arevery similar to the previously measured pattern for two-, four-, six,- and eight-particle single harmoniccumulants in Pb–Pb collisions [21], which show positive, negative, positive, and negative signs, respec-tively. These findings agree qualitatively with the initial-state predictions based on the MC-Glauber [38],AMPT, and TRENTo models [53]. It should be pointed out that the measured negative nMHC ( v , v ) shown above could only confirm the negative correlations of ( v , v ) , while the results presented inFig. 4 illustrate further the positive correlations of ( v , v ) and ( v , v ) as well as the negative correla-tions of ( v , v ) , ( v , v ) and ( v , v ) . Moreover, one can see the following hierarchy, | nMHC ( v , v ) | > | nMHC ( v , v ) | ≥ | nMHC ( v , v ) | > | nMHC ( v , v ) | ≈ | nMHC ( v , v ) | > | nMHC ( v , v ) | . This agreesqualitatively with the predictions based on initial-state models [38, 53]. Furthermore, the calculationsbased on the HIJING model [40], which does not generate anisotropic flow in the created system,are consistent with zero [38], and thus do not reproduce the characteristic signs of the multiparticlemixed harmonic cumulants observed in experiments. Future studies with other non-flow models, i.e.PYTHIA [56, 57], could confirm if the aforementioned characteristic signs of the multiparticle mixedharmonic cumulants can be regarded as a flow signature and thus could be used for searching for collec-tive flow in small collision systems like pp or pA collisions [58–60].As mentioned above, for non-peripheral collisions, both v and v are expected to be linearly corre-lated with the initial eccentricity ε and ε . Thus, the final-state result of nMHC ( v k , v l ) could reflectthe initial correlation between ε k and ε l . This behavior is observed in the case of nMHC ( v , v ) , wheregood agreement with nMHC ( ε , ε ) was found. Moving to higher moments of v and/or v , one canfurther probe the nonlinearity of v ( v ) to ε ( ε ) by seeing if the agreement between the initial andfinal-state correlations persists, because of the better sensitivity of higher moments to the nonlinear hy-drodynamic response. Figure 5 presents the comparison of data with iEBE-VISHNU calculations with10ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration − − − ) , v n M HC ( v ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC
Centrality percentile12 H y d r o / D a t a − − ) , v n M HC ( v ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC H y d r o / D a t a Figure 6:
Centrality dependence of nMHC ( v , v ) (left) and nMHC ( v , v ) (right) in Pb–Pb collisions at √ s NN = .
02 TeV. Statistical uncertainties are shown as vertical bars and systematic uncertainties as filled boxes.
AMPT and TRENTo initial conditions. This figure shows that both calculations describe the measured nMHC ( v , v ) fairly well for central and semi-central collisions. The calculations with AMPT initialconditions work better for more peripheral collisions. At the same time, consistent results are observedbetween nMHC ( ε , ε ) and nMHC ( v , v ) , independent of whether the AMPT or TRENTo initial-statemodel are used. For AMPT calculations, there is no difference between the results using η / s = .
08 or0.20, which confirms that the precision measurement of nMHC ( v , v ) can offer an additional approachto constrain initial-state models. However, the situation is different in the case of nMHC ( v , v ) , shownin Fig. 5 (right). The hydrodynamic calculations with both AMPT and TRENTo initial conditions arecompatible with the measurement within the considerable uncertainty, but there is an apparent discrep-ancy between nMHC ( v , v ) and nMHC ( ε , ε ) . This does not agree with the naive expectation of both v and v being linearly correlated with their respective initial eccentricities ε and ε , which might bebecause, generally, the linearity of v to ε is worse than that of v to ε as shown by hydrodynamiccalculations [7]. When one examines higher-order moments, the linear response of v remains and thus nMHC ( ε , ε ) = nMHC ( v , v ) is observed. However, the nonlinearity of v becomes non-negligible innon-peripheral collisions, which creates the discrepancy between the initial nMHC ( ε , ε ) and final state nMHC ( v , v ) correlations.This hypothesis is further confirmed in Figs. 6 and 7 where eight-particle cumulants are reported, whichinvolve even higher moments of v and/or v . Firstly, hydrodynamic calculations with AMPT initial con-ditions quantitatively predict the new measurements of nMHC ( v , v ) , nMHC ( v , v ) and nMHC ( v , v ) ,while the TRENTo calculations show compatible results except for nMHC ( v , v ) , where the calculationsoverestimate the data by a factor of two. Secondly, although in hydrodynamic calculations with two dif-ferent initial conditions there is a similar centrality dependence of nMHC ( ε , ε ) and nMHC ( v , v ) , aclear difference between the two is observed already in semi-central collisions. This difference becomesmuch larger when fourth and sixth order moments of v are involved, with no obvious agreement be-tween the initial and final-state calculations; this is especially shown by the TRENTo calculations inFigs. 6 (right) and 7. It is expected that the effect of the nonlinearity of v and v will be enhancedwhen studying nMHC ( v k , v l ) with higher moments (e.g. k , l ≥ nMHC ( v k , v l ) in thefinal state, instead of being determined solely by the initial correlations of nMHC ( ε k , ε l ) , receive non-11ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration − ) , v n M HC ( v ALICE Pb-Pb5.02 TeViEBE-VISHNU /s(T) ζ /s(T), η TRENTo-IC, TRENTo-IC/s = 0.08 η AMPT-IC, /s = 0.20 η AMPT-IC, AMPT-IC | < 0.8 η , | c < 5.0 GeV/ T p Figure 7:
Centrality dependence of nMHC ( v , v ) in Pb–Pb collisions at √ s NN = .
02 TeV. Statistical uncertaintiesare shown as vertical bars and systematic uncertainties as filled boxes. negligible contributions from the nonlinearities of higher moments of v and v , developed during thedynamic evolution of the system. Thus, the new measurements of nMHC ( v k , v l ) presented in this Letterprovide direct access to the initial correlations between ε k and ε l when lower moments of v and v areinvolved, while enabling a new possibility to study the nonlinearities of v and v when higher momentsare involved. The normalized mixed harmonic cumulants nMHC between two and three flow coefficients as well asbetween higher moments of two flow coefficients, were measured in √ s NN = .
02 TeV Pb–Pb colli-sions with ALICE. It is found that nMHC ( v , v ) is positive, while nMHC ( v , v ) and nMHC ( v , v ) arenegative. In addition, the first measurement of three harmonic correlations nMHC ( v , v , v ) is closerto nMHC ( v , v ) and nMHC ( v , v ) in central collisions, and then becomes closer to nMHC ( v , v ) and nMHC ( v , v ) for more peripheral collisions. These measurements compared with iEBE-VISHNU hy-drodynamic calculations using AMPT and TRENTo initial conditions exhibit different sensitivities to theinitial conditions and the specific shear viscosity of the QGP. Thus the measurements presented in thisLetter can be used to more tightly constrain theoretical models. Furthermore, the correlations betweenhigher moments of v and v were investigated for the first time. The four-, six- and eight-particle mixedcumulants of nMHC show the characteristic signature of negative, positive, and negative signs, respec-tively, similar to the multiparticle cumulants of single harmonics. The comparison with hydrodynamiccalculations reveals that the correlations involving higher-order moments could significantly enhance thecontributions that arise from nonlinearities of v and v to the initial eccentricity ε , triangularity ε ,respectively. Such contributions mainly develop during the expansion of the system and reflect the timeevolution of the shear and bulk viscosities of the QGP. These new measurements of correlations betweendifferent moments of two and three flow coefficients, together with comparisons to state-of-the-art hy-drodynamic calculations, provide further information on the initial conditions and considerably tightenthe constraints on the evolution of the QGP created in heavy-ion collisions at the LHC.12ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration Acknowledgments
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 HighTechnologies, 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 Education andScience, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technol-ogy Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry ofEducation and Scientific Research, Institute of Atomic Physics and Ministry of Research and Innova-tion and Institute of Atomic Physics, Romania; Joint Institute for Nuclear Research (JINR), Ministry ofEducation and Science of the Russian Federation, National Research Centre Kurchatov Institute, Rus-sian Science Foundation and Russian Foundation for Basic Research, Russia; Ministry of Education,Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of SouthAfrica, South Africa; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW),Sweden; European Organization for Nuclear Research, Switzerland; Suranaree University of Technology(SUT), National Science and Technology Development Agency (NSDTA) and Office of the Higher Edu-cation Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK),Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Coun-cil (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) andUnited States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America.13ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration
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S. Acharya , D. Adamová , A. Adler , J. Adolfsson , G. Aglieri Rinella , M. Agnello ,N. Agrawal , Z. Ahammed , S. Ahmad , S.U. Ahn , Z. Akbar , A. Akindinov ,M. Al-Turany , D. Aleksandrov , B. Alessandro , H.M. Alfanda , R. Alfaro Molina , B. Ali ,Y. Ali , A. Alici , N. Alizadehvandchali , A. Alkin , J. Alme , T. Alt , L. Altenkamper ,I. Altsybeev , M.N. Anaam , C. Andrei , D. Andreou , A. Andronic , V. Anguelov ,F. Antinori , P. Antonioli , C. Anuj , N. Apadula , L. Aphecetche , H. Appelshäuser ,S. Arcelli , R. Arnaldi , I.C. Arsene , M. Arslandok , , A. Augustinus , R. Averbeck ,S. Aziz , M.D. Azmi , A. Badalà , Y.W. Baek , X. Bai , R. Bailhache , Y. Bailung , R. Bala ,A. Balbino , A. Baldisseri , M. Ball , D. Banerjee , R. Barbera , L. Barioglio , , M. Barlou ,G.G. Barnaföldi , L.S. Barnby , V. Barret , C. Bartels , K. Barth , E. Bartsch , F. Baruffaldi ,N. Bastid , S. Basu , , G. Batigne , B. Batyunya , D. Bauri , J.L. Bazo Alba ,I.G. Bearden , C. Beattie , I. Belikov , A.D.C. Bell Hechavarria , F. Bellini , R. Bellwied ,S. Belokurova , V. Belyaev , G. Bencedi , , S. Beole , A. Bercuci , Y. Berdnikov ,A. Berdnikova , D. Berenyi , L. Bergmann , M.G. Besoiu , L. Betev , P.P. Bhaduri ,A. Bhasin , I.R. Bhat , M.A. Bhat , B. Bhattacharjee , P. Bhattacharya , L. Bianchi ,N. Bianchi , J. Bielˇcík , J. Bielˇcíková , J. Biernat , A. Bilandzic , G. Biro , S. Biswas ,J.T. Blair , D. Blau , M.B. Blidaru , C. Blume , G. Boca , F. Bock , A. Bogdanov , S. Boi ,J. Bok , L. Boldizsár , A. Bolozdynya , M. Bombara , P.M. Bond , G. Bonomi , H. Borel ,A. Borissov , H. Bossi , E. Botta , L. Bratrud , P. Braun-Munzinger , M. Bregant , M. Broz ,G.E. Bruno , , M.D. Buckland , D. Budnikov , H. Buesching , S. Bufalino , O. Bugnon ,P. Buhler , Z. Buthelezi , , J.B. Butt , S.A. Bysiak , D. Caffarri , M. Cai , , A. Caliva ,E. Calvo Villar , J.M.M. Camacho , R.S. Camacho , P. Camerini , F.D.M. Canedo ,A.A. Capon , F. Carnesecchi , R. Caron , J. Castillo Castellanos , E.A.R. Casula ,F. Catalano , C. Ceballos Sanchez , P. Chakraborty , S. Chandra , W. Chang , S. Chapeland ,M. Chartier , S. Chattopadhyay , S. Chattopadhyay , A. Chauvin , T.G. Chavez ,C. Cheshkov , B. Cheynis , V. Chibante Barroso , D.D. Chinellato , S. Cho , P. Chochula ,P. Christakoglou , C.H. Christensen , P. Christiansen , T. Chujo , C. Cicalo , L. Cifarelli ,F. Cindolo , M.R. Ciupek , G. Clai II , , J. Cleymans , F. Colamaria , J.S. Colburn ,D. Colella , , , , A. Collu , M. Colocci , , M. Concas III , , G. Conesa Balbastre , Z. Conesadel Valle , G. Contin , J.G. Contreras , T.M. Cormier , P. Cortese , M.R. Cosentino , F. Costa ,S. Costanza , P. Crochet , E. Cuautle , P. Cui , L. Cunqueiro , A. Dainese , F.P.A. Damas , ,M.C. Danisch , A. Danu , I. Das , P. Das , P. Das , S. Das , S. Dash , S. De , A. De Caro ,G. de Cataldo , L. De Cilladi , J. de Cuveland , A. De Falco , D. De Gruttola , N. De Marco ,C. De Martin , S. De Pasquale , S. Deb , H.F. Degenhardt , K.R. Deja , L. Dello Stritto ,S. Delsanto , W. Deng , P. Dhankher , D. Di Bari , A. Di Mauro , R.A. Diaz , T. Dietel ,Y. Ding , R. Divià , D.U. Dixit , Ø. Djuvsland , U. Dmitrieva , J. Do , A. Dobrin , B. Dönigus ,O. Dordic , A.K. Dubey , A. Dubla , , S. Dudi , M. Dukhishyam , P. Dupieux ,T.M. Eder , R.J. Ehlers , V.N. Eikeland , D. Elia , B. Erazmus , F. Ercolessi , F. Erhardt ,A. Erokhin , M.R. Ersdal , B. Espagnon , G. Eulisse , D. Evans , S. Evdokimov ,L. Fabbietti , M. Faggin , J. Faivre , F. Fan , A. Fantoni , M. Fasel , P. Fecchio , A. Feliciello ,G. Feofilov , A. Fernández Téllez , A. Ferrero , A. Ferretti , V.J.G. Feuillard , J. Figiel ,S. Filchagin , D. Finogeev , F.M. Fionda , G. Fiorenza , F. Flor , A.N. Flores , S. Foertsch ,P. Foka , S. Fokin , E. Fragiacomo , U. Fuchs , N. Funicello , C. Furget , A. Furs ,J.J. Gaardhøje , M. Gagliardi , A.M. Gago , A. Gal , C.D. Galvan , P. Ganoti ,C. Garabatos , J.R.A. Garcia , E. Garcia-Solis , K. Garg , C. Gargiulo , A. Garibli ,K. Garner , P. Gasik , E.F. Gauger , A. Gautam , M.B. Gay Ducati , M. Germain ,J. Ghosh , P. Ghosh , S.K. Ghosh , M. Giacalone , P. Gianotti , P. Giubellino , , P. Giubilato ,A.M.C. Glaenzer , P. Glässel , V. Gonzalez , L.H. González-Trueba , S. Gorbunov ,18ixed Harmonic Cumulants in Pb–Pb collisions ALICE CollaborationL. Görlich , S. Gotovac , V. Grabski , L.K. Graczykowski , K.L. Graham , L. Greiner ,A. Grelli , C. Grigoras , V. Grigoriev , A. Grigoryan I , , S. Grigoryan , , O.S. Groettvik ,F. Grosa , J.F. Grosse-Oetringhaus , R. Grosso , G.G. Guardiano , R. Guernane ,M. Guilbaud , M. Guittiere , K. Gulbrandsen , T. Gunji , A. Gupta , R. Gupta ,I.B. Guzman , M.K. Habib , C. Hadjidakis , H. Hamagaki , G. Hamar , M. Hamid ,R. Hannigan , M.R. Haque , , A. Harlenderova , J.W. Harris , A. Harton ,J.A. Hasenbichler , H. Hassan , D. Hatzifotiadou , P. Hauer , L.B. Havener , S. Hayashi ,S.T. Heckel , E. Hellbär , H. Helstrup , T. Herman , E.G. Hernandez , G. Herrera Corral ,F. Herrmann , K.F. Hetland , H. Hillemanns , C. Hills , B. Hippolyte , B. Hohlweger , ,J. Honermann , G.H. Hong , D. Horak , S. Hornung , R. Hosokawa , P. Hristov , C. Huang ,C. Hughes , P. Huhn , T.J. Humanic , H. Hushnud , L.A. Husova , N. Hussain , D. Hutter ,J.P. Iddon , , R. Ilkaev , H. Ilyas , M. Inaba , G.M. Innocenti , M. Ippolitov , A. Isakov , ,M.S. Islam , M. Ivanov , V. Ivanov , V. Izucheev , B. Jacak , N. Jacazio , P.M. Jacobs ,S. Jadlovska , J. Jadlovsky , S. Jaelani , C. Jahnke , , M.J. Jakubowska , M.A. Janik ,T. Janson , M. Jercic , O. Jevons , F. Jonas , , P.G. Jones , J.M. Jowett , , J. Jung ,M. Jung , A. Junique , A. Jusko , P. Kalinak , A. Kalweit , V. Kaplin , S. Kar , A. KarasuUysal , D. Karatovic , O. Karavichev , T. Karavicheva , P. Karczmarczyk , E. Karpechev ,A. Kazantsev , U. Kebschull , R. Keidel , M. Keil , B. Ketzer , Z. Khabanova , A.M. Khan ,S. Khan , A. Khanzadeev , Y. Kharlov , A. Khatun , A. Khuntia , B. Kileng , B. Kim , ,D. Kim , D.J. Kim , E.J. Kim , J. Kim , J.S. Kim , J. Kim , J. Kim , J. Kim , M. Kim ,S. Kim , T. Kim , S. Kirsch , I. Kisel , S. Kiselev , A. Kisiel , J.L. Klay , J. Klein , S. Klein ,C. Klein-Bösing , M. Kleiner , T. Klemenz , A. Kluge , A.G. Knospe , C. Kobdaj ,M.K. Köhler , T. Kollegger , A. Kondratyev , N. Kondratyeva , E. Kondratyuk , J. Konig ,S.A. Konigstorfer , P.J. Konopka , , G. Kornakov , S.D. Koryciak , L. Koska , O. Kovalenko ,V. Kovalenko , M. Kowalski , I. Králik , A. Kravˇcáková , L. Kreis , M. Krivda , ,F. Krizek , K. Krizkova Gajdosova , M. Kroesen , M. Krüger , E. Kryshen , M. Krzewicki ,V. Kuˇcera , C. Kuhn , P.G. Kuijer , T. Kumaoka , L. Kumar , S. Kundu , , P. Kurashvili ,A. Kurepin , A.B. Kurepin , A. Kuryakin , S. Kushpil , J. Kvapil , M.J. Kweon , J.Y. Kwon ,Y. Kwon , S.L. La Pointe , P. La Rocca , Y.S. Lai , A. Lakrathok , M. Lamanna , R. Langoy ,K. Lapidus , P. Larionov , E. Laudi , L. Lautner , , R. Lavicka , T. Lazareva , R. Lea , ,J. Lee , J. Lehrbach , R.C. Lemmon , I. León Monzón , E.D. Lesser , M. Lettrich , ,P. Lévai , X. Li , X.L. Li , J. Lien , R. Lietava , B. Lim , S.H. Lim , V. Lindenstruth ,A. Lindner , C. Lippmann , A. Liu , J. Liu , I.M. Lofnes , V. Loginov , C. Loizides ,P. Loncar , J.A. Lopez , X. Lopez , E. López Torres , J.R. Luhder , M. Lunardon ,G. Luparello , Y.G. Ma , A. Maevskaya , M. Mager , T. Mahmoud , A. Maire , R.D. Majka I , ,M. Malaev , Q.W. Malik , L. Malinina IV , , D. Mal’Kevich , N. Mallick , P. Malzacher ,G. Mandaglio , , V. Manko , F. Manso , V. Manzari , Y. Mao , J. Mareš , G.V. Margagliotti ,A. Margotti , A. Marín , C. Markert , M. Marquard , N.A. Martin , P. Martinengo ,J.L. Martinez , M.I. Martínez , G. Martínez García , S. Masciocchi , M. Masera , A. Masoni ,L. Massacrier , A. Mastroserio , , A.M. Mathis , O. Matonoha , P.F.T. Matuoka ,A. Matyja , C. Mayer , A.L. Mazuecos , F. Mazzaschi , M. Mazzilli , , M.A. Mazzoni ,A.F. Mechler , F. Meddi , Y. Melikyan , A. Menchaca-Rocha , 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 , 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 , J. 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 , A. Neagu ,L. Nellen , S.V. Nesbo , G. Neskovic , D. Nesterov , B.S. Nielsen , S. Nikolaev , S. Nikulin ,19ixed Harmonic Cumulants in Pb–Pb collisions ALICE CollaborationV. 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. OliveiraDa 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.P. Pathak ,B. Paul , J. Pazzini , H. Pei , T. Peitzmann , X. Peng , L.G. Pereira , H. Pereira Da Costa ,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 , S. Politano , 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 , H.A. Reme-ness ,R. Renfordt , Z. Rescakova , K. Reygers , A. Riabov , V. Riabov , T. Richert , , M. Richter ,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 ,T.J. Shaba , A. Shabanov , A. Shabetai , R. Shahoyan , W. Shaikh , A. Shangaraev ,A. Sharma , H. Sharma , M. Sharma , N. Sharma , S. Sharma , O. Sheibani , K. Shigaki ,M. Shimomura , S. Shirinkin , Q. Shou , Y. Sibiriak , S. Siddhanta , T. Siemiarczuk ,T.F. Silva , D. Silvermyr , 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 , A. Uras , M. Urioni , G.L. Usai , M. Vala , N. Valle , S. Vallero , N. van derKolk , 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. Vázquez Doce ,V. Vechernin , E. Vercellin , S. Vergara Limón , L. Vermunt , R. Vértesi , M. 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 ,20ixed Harmonic Cumulants in Pb–Pb collisions ALICE CollaborationA. 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. 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, Norway 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, Italy21ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration 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,Netherlands 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, India22ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration 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 fürSchwerionenforschung GmbH, Darmstadt, Germany
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 Kingdom23ixed Harmonic Cumulants in Pb–Pb collisions ALICE Collaboration
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 Kansas, Lawrence, Kansas, United States
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