Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at √sNN = 2.76 TeV

This is an electronic reprint of the original article. This reprint may differ from the original in pagination and typographic detail. Author(s): Title: Year: Version: Please cite the original version: All material supplied via JYX is protected by copyright and other intellectual property rights, and duplication or sale of all or part of any of the repository collections is not permitted, except that material may be duplicated by you for your research use or educational purposes in electronic or print form. You must obtain permission for any other use. Electronic or print copies may not be offered, whether for sale or otherwise to anyone who is not an authorised user. Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at √sNN = 2.76 TeV ALICE Collaboration ALICE Collaboration. (2018). Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at √sNN = 2.76 TeV. Physical Review C, 97(2), Article 024906. https://doi.org/10.1103/PhysRevC.97.024906 2018 PHYSICAL REVIEW C 97, 024906 (2018) Systematic studies of correlations between different order flow harmonics in Pb-Pb collisions at √sNN =2.76 TeV S. Acharya et al.∗ (ALICE Collaboration) (Received 1 October 2017; published 12 February 2018) The correlations between event-by-event fluctuations of anisotropic flow harmonic amplitudes have been measured in Pb-Pb collisions at √sNN =2.76 TeV with the ALICE detector at the Large Hadron Collider. The results are reported in terms of multiparticle correlation observables dubbed symmetric cumulants. These observables are robust against biases originating from nonflow effects. The centrality dependence of correlations between the higher order harmonics (the quadrangular v4and pentagonal v5flow) and the lower order harmonics (the elliptic v2and triangular v3flow) is presented. The transverse momentum dependences of correlations between v3and v2and between v4and v2are also reported. The results are compared to calculations from viscous hydrodynamics and a multiphase transport (AMPT) model calculations. The comparisons to viscous hydrodynamic models demonstrate that the different order harmonic correlations respond differently to the initial conditions and the temperature dependence of the ratio of shear viscosity to entropy density (η/s). A small average value of η/s is favored independent of the specific choice of initial conditions in the models. The calculations with the AMPT initial conditions yield results closest to the measurements. Correlations among the magnitudes of v2,v3,andv4show moderate pTdependence in midcentral collisions. This might be an indication of possible viscous corrections to the equilibrium distribution at hadronic freeze-out, which might help to understand the possible contribution of bulk viscosity in the hadronic phase of the system. Together with existing measurements of individual flow harmonics, the presented results provide further constraints on the initial conditions and the transport properties of the system produced in heavy-ion collisions. DOI: 10.1103/PhysRevC.97.024906 I. INTRODUCTION The main emphasis of the ultrarelativistic heavy-ion collision programs at the Relativistic Heavy Ion Collider (RHIC) andtheLargeHadronCollider(LHC)istostudythedeconfined phase of strongly interacting QCD matter, the quark-gluon plasma (QGP). The matter produced in a heavy-ion collision exhibits strong collective radial expansion [1,2]. Difference in pressure gradients and the interactions among matter constituents produced in the spatially anisotropic overlap region of the two colliding nuclei result in anisotropic transverse flow in the momentum space. The large elliptic flow discovered at RHIC energies [3–7] is also observed at LHC energies [8–18]. The measurements are well described by calculations utilizing viscous hydrodynamics [19–24]. These calculations alsodemonstratedthattheshearviscositytotheentropydensity ratio (η/s) of the QGP in heavy-ion collisions at RHIC and LHC energies is close to a universal lower bound 1/4π[25]. The temperature dependence of η/s has some generic features typical to the most known fluids. This ratio reaches ∗Full author list given at the end of the article. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. its minimum value close to the phase transition region [25,26]. It was shown, using kinetic theory and quantum mechanical considerations [27], that η/s ∼0.1 would be the correct order of magnitude for the lowest possible shear viscosity to entropy density ratio value found in nature. Later it was demonstrated that an exact lower bound (η/s)min =1/4π≈ 0.08 can be conjectured using anti-de sitter/conformal field theory(AdS/CFT) correspondence[25]. Hydrodynamicalsimulations constrained by data support the view that η/s of the QGP is close to that limit [23]. It is argued that such a low value might imply that thermodynamic trajectories for the expanding matter would lie close to the quantum chromodynamics (QCD) critical end point, which is another subject of intensive experimental study [26,28]. Anisotropic flow [29] is quantified with nth-order flow harmonics vnand corresponding symmetry plane angles nin a Fourier decomposition of the particle azimuthal distribution in the plane transverse to the beam direction [30,31]: Ed3N d3p=1 2π d2N pTdpTdη ×1+2∞  n=1 vn(pT,η) cos[n(ϕ−n)],(1) where E,p,pT,ϕ, and ηare the particle’s energy, momentum, transverse momentum, azimuthal angle, and pseudorapidity, respectively, and nis the azimuthal angle of the symmetry 2469-9985/2018/97(2)/024906(23) 024906-1 ©2018 CERN, for the ALICE Collaboration S. ACHARYA et al. PHYSICAL REVIEW C 97, 024906 (2018) planeofthenth-orderharmonic.Harmonicvncanbecalculated as vn=cos[n(ϕ−n)], where the angular brackets denote an average over all particles in all events. The anisotropic flow in heavy-ion collisions is typically understood as the hydrodynamic response of the produced matter to spatial deformations of the initial energy density profile [32]. This profile fluctuates event by event due to fluctuating positions of the constituents inside the colliding nuclei, which implies that vnalso fluctuates [33,34]. The recognition of the importance of flow fluctuations led to the discovery of triangular and higher flow harmonics [9,35] as well as to the correlations between different vnharmonics [36,37]. The higher order harmonics are expected to be sensitive to fluctuations in the initial conditions and to the magnitude of η/s [38,39], while vncorrelations have the potential to discriminate between these two respective contributions [36]. Difficulties in extracting η/s in heavy-ion collisions can be attributed mostly to the fact that it strongly depends on the specific choice of the initial conditions in the models used for comparison [19,39,40]. Viscous effects reduce the magnitude of the anisotropic flow. Furthermore, the magnitude of η/s used in hydrodynamic calculations should be considered as an average over the temperature evolution of the expanding fireball as it is known that η/s depends on temperature. In addition, part of the anisotropic flow can also originate from the hadronic phase [41–43]. Therefore, both the temperature dependence of η/s and the relative contributions from the partonic and hadronic phases should be understood better to quantify the η/s of the QGP. An important input to the hydrodynamic model simulations is the initial distribution of energy density in the transverse plane (the initial density profile), which is usually estimated from the probability distribution of nucleons in the incoming nuclei. This initial energy density profile can be quantified by calculating the distribution of the spatial eccentricities n[35], εneinn=−{rneinφ}/{rn},(2) where the curly brackets denote the average over the transverse plane, i.e., {···}=dxdy e(x,y,τ0)(···), ris the distance to the system’s center of mass, φis azimuthal angle, e(x,y,τ0)is theenergydensityat theinitialtimeτ0,and nistheparticipant plane angle (see Refs. [44,45]). There is experimental and theoretical evidence [9,35,46] that the lower order harmonics, v2and v3, to a good approximation, are linearly proportional to the deformations in the initial energy density in the transverse plane (e.g., vn∝εnfor n=2 or 3). Higher order (n>3) flow harmonics can arise from initial anisotropies in the same harmonic [35,44,47,48] (linear response) or can be induced by lower order harmonics [49,50] (nonlinear response). For instance, v4can develop both as a linear response to ε4and/or as a nonlinear response to ε2 2[51]. Therefore, the higher harmonics (n>3) can be understood as superpositions of linear and nonlinear responses, through which they are correlated with lower order harmonics [47,48,50,52,53]. When the order of the harmonic is large, the nonlinear response contribution in viscous hydrodynamics is dominant and increases in more peripheral collisions [50,52]. The magnitudes of the viscous corrections as a function of pTfor v4and v5are sensitive to the ansatz used for the viscous distribution function, a correction for the equilibrium distribution at hadronic freeze-out [52,54]. Hence,studiesofthecorrelationsbetweenhigher order(n>3) and lower order (v2or v3) harmonics and their pTdependence can help to understand the viscous correction to the momentum distribution at hadronic freeze-out which is among the least understood parts of hydrodynamic calculations [45,52,55,56]. The first results for new multiparticle observables which quantify the relationship between event-by-event fluctuations of two different flow harmonics, the symmetric cumulants (SC), were recently reported by the ALICE Collaboration [57]. The new observables are particularly robust against few-particle nonflow correlations [8] and they provide independent, complementary information to recently analyzed symmetry plane correlators [37]. It was demonstrated that they are sensitive to the temperature dependence of η/s of the expanding medium and therefore simultaneous descriptions of correlations between different order harmonics would constrain both the initial conditions and the medium properties [57,58]. In this article, we have extended the analysis of SC observables tohigher orderharmonics (upto fifthorder) aswell as to the measurement of the pTdependence of correlations for the lower order harmonics (v3-v2and v4-v2). We also present a systematic comparison to hydrodynamic and AMPT model calculations. In Sec. II we present the analysis methods and summarize our findings from the previous work [57]. The experimental setup and measurements are described in Sec. III. The sources of systematic uncertainties are explained in Sec. IV. The results of the measurements are presented in Sec. V. In Sec. VI we present comparisons to model calculations. Finally, Sec. VII summarizes our new results. II. EXPERIMENTAL OBSERVABLES Existing measurements for anisotropic flow observables provide an estimate of the average value of η/s of the QGP, both at RHIC and LHC energies. What remains uncertain is how the η/s of the QGP depends on temperature (T). The temperature dependence of η/s of the QGP was discussed in Ref. [28]. The effects on hadron spectra and elliptic flow were studied in Ref. [59] for different parametrizations of η/s(T). Amore systematicstudywith event-by-eventEskola-Kajantie- Ruuskanen-Tuominen (EKRT) +viscous hydrodynamic calculations was recently initiated in Ref. [45], where the first (andonly ratherqualitative)possibilities wereinvestigated(see Fig. 1therein). The emerging picture is that the study of individual flow harmonics vnalone is unlikely to reveal the details of the temperature dependence of η/s. It was already demonstrated in Ref. [45] that different η/s(T) parametrizations can lead to the same centrality dependence of individual flow harmonics. In Ref. [36] new flow observables were introduced which quantify the degree of correlation between amplitudes of two different harmonics vmand vn. These new observables have the potential to discriminate between the contributions to anisotropic flow development from initial conditions and from the transport properties of the QGP [36]. Therefore, their measurement would provide experimental constraints on theoretical parameters used to describe the individual stages of the heavy-ion system evolution. In addition, it turned out that correlations of different flow harmonics are sensitive to 024906-2 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 0 1020304050 Centrality percentile 0.1− 0 0.1 0.2 0.3 6− 10× )n,mSC( (a) c < 5.0 GeV/ T p| < 0.8, 0.2 < η| = 2.76 TeV NN sALICE Pb-Pb 0.1) PRL 117 (2016) 182301×SC(3,2) ( 0.1) PRL 117 (2016) 182301×SC(4,2) ( SC(5,2) SC(5,3) SC(4,3) 0 1020304050 Centrality percentile 0.5− 0 0.5 1 1.5 )n , mNSC( (b) c < 5.0 GeV/ T p| < 0.8, 0.2 < η| = 2.76 TeV NN sALICE Pb-Pb NSC(3,2) PRL 117 (2016) 182301 NSC(4,2) PRL 117 (2016) 182301 NSC(5,2) NSC(5,3) NSC(4,3) FIG. 1. The centrality dependence of SC(m,n) (a) and NSC(m,n) (b) with flow harmonics for m=3−5andn=2,3 in Pb-Pb collisions at √sNN =2.76 TeV. The lower order harmonic correlations [SC(3,2), SC(4,2), NSC(3,2), and NSC(4,2)] are taken from Ref. [57]andshownas bands. The systematic and statistical errors are combined in quadrature for these lower order harmonic correlations. The SC(4,2) and SC(3,2) are downscaled by a factor of 0.1. Systematic uncertainties are represented with boxes for higher order harmonic correlations. the temperature dependence of η/s [57], to which individual flow harmonics are weakly sensitive [45]. For reasons discussed in Refs. [57,60], the correlations between different flow harmonics cannot be studied experimentally with the set of observables introduced in Ref. [36]. BasedonRef.[60], new flow observables obtained from multiparticle correlations, symmetric cumulants (SC), were introduced. The SC observables are defined as SC(m,n)≡cos(mϕ1+nϕ2−mϕ3−nϕ4)c =cos(mϕ1+nϕ2−mϕ3−nϕ4) −cos[m(ϕ1−ϕ2)]cos[n(ϕ1−ϕ2)] =v2 mv2 n−v2 mv2 n,(3) with the condition m= nfor two positive integers mand n (for details see Sec. IVC in Ref. [60]). In this article, SC(m,n) normalized by the product v2 mv2 n[57,61] is denoted by NSC(m,n): NSC(m,n)≡SC(m,n) v2 mv2 n.(4) Normalized symmetric cumulants reflect only the strength of the correlation between vmand vn, while SC(m,n) has contributions from both the correlations between the two different flow harmonics and the individual harmonics. In Eq. (4)the products in the denominator are obtained from two-particle correlations using a pseudorapidity gap of |η|>1.0 which suppresses biases from few-particle nonflow correlations. For the two two-particle correlations which appear in the definition of SC(m,n)inEq.(3), the pseudorapidity gap is not needed, since nonflow is suppressed by construction in this observable. This was verified by HIJING model simulations in Ref. [57]. The ALICE measurements [57] have revealed that fluctuations of v2and v3are anticorrelated, while fluctuations of v2 and v4are correlated for all centralities [57]. It was found that thedetails ofthecentrality dependencedifferin thefluctuationdominated (most central) and the geometry-dominated (midcentral) regimes [57]. The observed centrality dependence of SC(4,2) cannot be captured by models with constant η/s, indicating that the temperature dependence of η/s plays an important role. These results were also used to discriminate between different parametrizations of initial conditions. It was demonstrated that in the fluctuation-dominated regime (central collisions), Monte Carlo (MC)–Glauber initial conditions with binary collision weights are favored over wounded nucleon weights [57]. The first theoretical studies of SC observables can be found in Refs. [58,61–65]. III. DATA ANALYSIS The data sample of Pb-Pb collisions at the center-of-mass energy √sNN =2.76 TeV analyzed in this article was recorded by ALICE during the 2010 heavy-ion run of the LHC. Detailed descriptions of the ALICE detector can be found in Refs. [66–68]. The time projection chamber (TPC) was used to reconstruct charged particle tracks and measure their momenta with full azimuthal coverage in the pseudorapidity range |η|< 0.8. Two scintillator arrays (V0A and V0C) which cover the pseudorapidity ranges −3.7<η<−1.7 and 2.8<η<5.1 were used for triggering and the determination of centrality [69]. The trigger conditions and the event selection criteria are identical to those described in Refs. [8,69]. Approximately 107minimum-bias Pb-Pb events with a reconstructed primary vertex within ±10 cm from the nominal interaction point along the beam direction are selected. Only charged particles reconstructed in the TPC in |η|<0.8 and 0.2<p T<5GeV/c were included in the analysis. The charged track quality cuts described in Ref. [8] were applied to minimize contamination from secondary charged particles and fake tracks. The track reconstruction efficiency and contamination were estimated from HIJING Monte Carlo simulations [70] combined with a GEANT3[71] detector model and were found to be independent of the collision centrality. The reconstruction efficiency increases with transverse momenta from 70% to 80% for particles with 0.2<p T<1GeV/c and remains constant at (80 ±5)% for pT>1GeV/c. The estimated contamination 024906-3 S. ACHARYA et al. PHYSICAL REVIEW C 97, 024906 (2018) by secondary charged particles from weak decays and photon conversions is less than 6% at pT=0.2GeV/c and falls below 1% for pT>1GeV/c. The pTcutoff of 0.2 GeV/c reduces event-by-event biases due to small reconstruction efficiency at lower pT, while the high pTcutoff of 5 GeV/c reduces the effects of jets on the measured correlations. Reconstructed TPC tracks constrained to vertex are required to have at least 70 space points (out of a maximum of 159). Only tracks with a transverse distance of closest approach to the primary vertex less than 3 mm, both in the longitudinal and transverse directions, are accepted. This reduces the contamination from secondary tracks produced in the detector material, particles from weak decays, etc. Tracks with kinks (i.e., tracks that appear to change direction due to multiple scattering or K± decays) were rejected. IV. SYSTEMATIC UNCERTAINTIES The systematic uncertainties are estimated by varying the event and track selection criteria. All systematic checks describedhere areperformed independently. TheSC(m,n)values resulting from each variation are compared to ones from the default event and track selection described in the previous section, and differences are taken as the systematic uncertainty due to each individual source. The contributions from different sources were added in quadrature to obtain the total systematic uncertainty. The event centrality was determined by the V0 detectors [72] with better than 2% resolution for the whole centrality range analyzed. The systematic uncertainty from the centrality determination was evaluated by using the TPC and silicon pixel detector (SPD) [73] detectors instead of the V0 detectors. The systematic uncertainty on the symmetric cumulants which arises from the centrality uncertainty is about 3% both for SC(5,2) and SC(4,3) and 8% for SC(5,3). As described in Sec. III, the reconstructed vertex position along the beam axis (zvertex) is required to be located within 10 cm of the nominal interaction to ensure uniform detector acceptance for tracks within |η|<0.8. The systematic uncertainty from the z-vertex cut was estimated by reducing the z-vertex range to 8 cm and was found to be less than 3%. The analyzed events were recorded with two settings of the magnet field polarity and the resulting data sets have almost equal numbers of events. Events with both magnet field polarities were used in the default analysis, and the systematic uncertainties were evaluated from the variation between each of the two magnetic field settings. The uncertainty due to the pTdependence of the track reconstruction efficiency was also taken into account. Magnetic field polarity variation and reconstruction efficiency effects contribute less than 2% to the systematic uncertainty. The systematic uncertainty due to the track reconstruction procedurewasestimatedfromcomparisons betweenresults for the so-called standalone TPC tracks with the same parameters as described in Sec. III, and tracks from a combination of the TPC and the inner tracking system (ITS) detectors with tighter selection criteria. To avoid nonuniform azimuthal acceptance due to dead zones in the SPD, and to get the best transverse momentum resolution, a hybrid track selection utilizing SPD hitsand/orITSrefittrackscombinedwithTPCinformationwas used. Then each track reconstruction strategy was evaluated by varying the threshold on parameters used to select the tracks at the reconstruction level. A systematic difference of up to 12% was observed in SC(m,n) from the different track selections. In addition, we applied the like-sign technique to estimate nonflow contributions [8]toSC(m,n). The difference between results obtained by selecting all charged particles and results obtained after either selecting only positively or only negatively charged particles was the largest contribution to the systematic uncertainty and is about 7% for SC(4,3) and 20% for SC(5,3). Another large contribution to the systematic uncertainty originates from azimuthal nonuniformities in the reconstruction efficiency. In order to estimate its effects, we use the AMPT model (see Sec. VI), which has a uniform distribution in azimuthal angle. Detector inefficiencies were introduced to mimic the nonuniform azimuthal distribution in the data. For the observables SC(5,2), SC(5,3), and SC(4,3), the variation due to nonuniform acceptance is about 9%, 17%, and 11%, respectively. Overall, the systematic uncertainties are larger for SC(5,3) and SC(5,2) than for the lower harmonics of SC(m,n). This is because vndecreases with increasing n and becomes more sensitive to azimuthal modulation due to detector imperfections. V. R E S U LT S The centrality dependence of the higher order harmonic correlations [SC(4,3), SC(5,2), and SC(5,3)] are presented in Fig. 1and compared to the lower order harmonic correlations [SC(3,2) and SC(4,2)], which were published in Ref. [57]. The correlation between v3and v4is negative, and similarly for v3and v2, while the other correlations are all positive, which reveals that v2and v5as well as v3and v5are correlated like v2and v4, while v3and v4are anticorrelated like v3and v2. The higher order flow harmonic correlations are much smaller compared to the lower order harmonic correlations. In particular, SC(5,2) is 10 times smaller than SC(4,2) and SC(4,3) is about 20 times smaller than SC(3,2). UnlikeSC(m,n),theNSC(m,n)resultswiththehigherorder flow harmonics show almost the same order of the correlation strength as the lower order flow harmonic correlations NSC(3,2) or NSC(4,2). This demonstrates the advantage of using the normalized SC observables in which the correlation strength between flow harmonics is not hindered by the differences in magnitudes of different flow harmonics. The NSC(4,3) magnitude is comparable to NSC(3,2) and one finds that a hierarchy, NSC(5,3) >NSC(4,2) >NSC(5,2), holds for the centrality range 20–50% within the errors as shown in Fig. 1(b). The SC(5,2) magnitude is larger than SC(5,3), but the normalized correlation between v5and v3is stronger than the normalized correlation between v5and v2. These results indicate that the lower order harmonic correlations are larger than higher order harmonic correlations, not only because of the correlation strength itself but also because of the strength of the individual flow harmonics. It can be seen in Fig. 1(a) that the lower order harmonic correlations as well as SC(5,2) increase nonlinearly toward 024906-4 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.05 0.1 3− 10× SC(4,2) 0 - 5% 5 - 10% 10 - 20% 20 - 30% 30 - 40% 40 - 50% (c) 0.06− 0.04− 0.02− 0 3− 10× SC(3,2) = 2.76 TeV NN sALICE Pb-Pb c < 5 GeV/ T p < T,min p| < 0.8, η| (a) 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 0 0.5 NSC(4,2) (d) 0.2− 0.15− 0.1− 0.05− 0 NSC(3,2) (b) ]c [GeV/ T,min p]c [GeV/ T,min p FIG. 2. SC(3,2) and SC(4,2) [panels (a) and (c)] as a function of minimum pTcuts in Pb-Pb collisions at √sNN =2.76 TeV are shown in the left panels. The NSC(3,2) and NSC(4,2) [panels (b) and (d)] are shown in the right panels. Systematic uncertainties are represented with boxes. peripheral collisions. In the case of SC(5,3) and SC(4,3), the centrality dependence is weaker than for the other harmonic correlations. The NSC(5,3) observable shows the strongest normalized correlation among all harmonics while NSC(5,2) shows the weakest centrality dependence. Both NSC(3,2) and NSC(4,3) are getting more anticorrelated toward peripheral collisions and have similar magnitudes. To study the pTdependence of SC(m,n), we present the results as a function of the low pTcutoff (pT,min), instead of using independent pTintervals; this decreases large statistical fluctuations in the results. Various minimum pTcuts from 0.2 to 1.5 GeV/c are applied. The pTdependent results for SC(3,2) and SC(4,2) as a function of minimum pTcuts are shown in Figs. 2(a) and 2(c). The strength of SC(m,n) becomes larger as pT,min increases. The centrality dependence is stronger with higher pT,min cuts, with SC(m,n) getting much larger as centrality percentile or pT,min increases. The NSC(3,2) and NSC(4,2) observables with different pT,min are shown in Figs. 2(b) and 2(d). The strong pT,min dependence observed in SC(m,n) is not seen in NSC(m,n). This indicates that the pT dependence of SC(m,n) is dominated by the pTdependence of the individual flow harmonics vn.ThepT,min dependence of NSC(3,2) is not clearly seen and it is consistent with no pT,min dependence within the statistical and systematic errors for the centrality range 0–30%, while showing a moderate increase of anticorrelation with increasing pT,min for the 30–50% centrality range. The NSC(4,2) observable shows a moderate decreasing trend as pT,min increases. These observations are strikingly different from the pTdependence of the individual flow harmonics, where the relative flow fluctuations σv2/v2 [74] are independent of transverse momentum up to pT ∼8GeV/c (see Fig. 3 in Ref. [75]). As discussed in Sec. II,theNSC(m,n) observables are normalized by the product v2 mv2 n. These products are obtained from two-particle correlations using a pseudorapidity gap of |η|>1.0. In this paper, we denote the pTintegrated vn{2,|η|>1}as vnin the transverse momentum range 0.2< pT<5.0GeV/c. The individual flow harmonics vnused in calculations of the NSC observables are shown in Fig. 3. The centrality dependence of vnfor n=2−5isshownin Figs. 3(a)–3(c).Thevnvalues (n<5) are equivalent to those in Ref. [11]. The fifth-order flow harmonic v5is shown in Fig. 3(c).ThepT,min dependence of vnfor n=2−4isshownin Figs. 3(d)–3(f) in all centrality ranges relevant to the measured NSC(m,n) observables. VI. MODEL COMPARISONS We have performed a systematic comparison of the centrality and transverse momentum dependence of the SC(m,n) and NSC(m,n) to the event-by-event EKRT+viscous hydrodynamics [45], VISH2+1[76,77], and the AMPT [63,78,79] models. Comparisons for vncoefficients with the model calculations are presented in the Appendix. In the event-by-event EKRT+viscous hydrodynamic calculations [45], the initial energy density profiles are calculated using a next-to-leading order perturbative-QCD +saturation model [80,81]. The subsequent space-time evolution is described by relativistic dissipative fluid dynamics with different parametrizations for the temperature dependence of the shear viscosity to entropy density ratio η/s(T). This model gives a good description of the charged hadron multiplicity and the low-pTregion of the charged hadron spectra at RHIC and the LHC (see Figs. 11–13 in Ref. [45]). Each of the η/s(T) 024906-5 S. ACHARYA et al. PHYSICAL REVIEW C 97, 024906 (2018) FIG. 3. The individual flow harmonics vnfor n=2−5 in Pb-Pb collisions at √sNN =2.76 TeV are shown in the left panels [(a), (b), and (c)]. v4and v5are shown in the same panel (c). The pT,min dependence of vnfor n=2−4 is shown in the right panels [(d), (e), and (f)]. parametrizationsis adjustedtoreproduce themeasuredvnfrom central to midperipheral collisions (see Fig. 15 in Ref. [45] and our Appendix). The VISH2+1[76,77] event-by-event calculations for relativistic heavy-ion collisions are based on (2+1)-dimensional viscous hydrodynamics which describes the QGP phase and the highly dissipative and off-equilibrium late hadronic stages with fluid dynamics. By tuning transport coefficients and decoupling temperature for a given scenario of initial conditions, it can describe the pTspectra and different flow harmonics at RHIC and the LHC [20,76,82,83] energies. Three different types of initial conditions [58] (MC-Glauber, Monte Carlo Kharzeev-Levin-Nardi (MC-KLN), and AMPT) along with different constant η/s values have been used for our data to model comparisons. Traditionally, the Glauber model constructs the initial entropy density from the wounded nucleon and binary collision density profiles [84]. The KLN model assumes that the initial energy density is proportional to that of the initial gluons calculated from the corresponding kTfactorization formula [85]. In Monte Carlo versions MC- Glauber and MC-KLN [86–88] of these models, additional initial state fluctuations are introduced through position fluctuations of individual nucleons inside the colliding nuclei. For the AMPT initial conditions [83,89,90], the fluctuating energy density profiles are constructed from the energy distribution of individual partons, which fluctuate in both momentum and coordinate space. Compared with the MC-Glauber and MC-KLN initial conditions, the additional Gaussian smearing intheAMPTinitialconditions givesrisetononvanishinginitial local flow velocities [89]. Even though thermalization could be achieved quickly in collisions of very large nuclei and/or at extremely high energy [91], the dense matter created in heavy-ion collisions may not reach full thermal or chemical equilibrium due to its finite size and short lifetime. To address such nonequilibrium many-body dynamics, the AMPT model [78,92,93] has been developed, which includes both initial partonic and final hadronic interactions and the transition between these two phases of matter. The initial conditions in the AMPT are given by the spatial and momentum distributions of minijets and soft strings from the HIJING model [70,94]. For the data comparisons, three different configurations of the AMPT model have been used: the default one and string melting with and without hadronic rescattering. The input parameters used in all configurations are αs=0.33 and a partonic cross section of 1.5 mb. In the default configuration, partons are recombined with their parent strings when they stop interacting. The resulting strings are later converted into hadrons using the Lund string fragmentation model [95,96]. The Lund string fragmentation parameters were set to α=0.5 024906-6 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 60− 40− 20− 09− 10× SC(4,3) (e) 0 20 40 60 9− 10× SC(5,3) (d) 0 0.05 0.1 0.15 0.2 6− 10× SC(5,2) (c) 0 1 2 6− 10× SC(4,2) EKRT+Viscous Hydrodynamics /s=0.2)ηparam0 ( /s(T))ηparam1 ( (b) 1.5− 1− 0.5− 0 6− 10× SC(3,2) = 2.76 TeV NN sPb-Pb c < 5.0 GeV/ T p| < 0.8, 0.2 < η| ALICE (a) 0.3− 0.2− 0.1− 0 NSC(4,3) (E) 0 0.5 1 1.5 NSC(5,3) (D) 0 0.2 0.4 NSC(5,2) (C) 0 0.5 NSC(4,2) (B) 0.15− 0.1− 0.05− 0 NSC(3,2) (A) 0 1020304050 10 20304050 Centrality percentile Centrality percentile FIG. 4. The centrality dependence of SC(m,n)andNSC(m,n) in Pb-Pb collisions at √sNN =2.76 TeV. Results are compared to the eventby-event EKRT+viscous hydrodynamic calculations [45]. The lines are hydrodynamic predictions with two different η/s(T) parametrizations. Left (right) panels show SC(m,n)(NSC(m,n)). and b=0.9GeV −2. In the string melting configuration, the initial strings are melted into partons whose interactions are described by the Zhang’s parton cascade (ZPC) model [97]. These partons are then combined into the final-state hadrons via a quark coalescence model. In both configurations, the dynamics of the subsequent hadronic matter is described by a hadronic cascade based on a relativistic transport (ART) model [98] which includes resonance decays. The string melting configuration of the AMPT without hadronic rescattering was used to study the influence of the hadronic phase on the development of the anisotropic flow. Even though the string melting version of AMPT [78,99] reasonably well reproduces particle yields, pTspectra, and v2of low-pTpions and kaons in central and midcentral Au-Au collisions at √sNN =200 GeV and Pb-Pb collisions at √sNN =2.76 TeV [79], it was observed in a recent study [100] that it fails to quantitatively reproduce the flow harmonics of identified hadrons (v2,v3,v4, and v5)at√sNN =2.76 TeV. It turns out that the radial flow in AMPT is 25% lower than that measured at the LHC, which is responsible for this quantitative disagreement [100]. The details of the AMPT configurations used in this article and the comparisons of pT-differential vnfor pions, kaons, and protons to the data can be found in Ref. [100]. A. Centrality dependence of SC(m,n) and NSC(m,n) Comparison to event-by-event EKRT+viscous hydrodynamic predictions with various parametrizations of the temperature dependence of η/s(T) was shown in Fig. 2 of Ref. [57]. It was demonstrated that NSC(3,2) is sensitive mainly to the initial conditions, while NSC(4,2) is sensitive to both the initial conditions and the system properties, which is consistent with the predictions from Ref. [36]. The model calculations for NSC(4,2) observable show that it has better sensitivity for different η/s(T) parametrizations but they cannot describe either the centrality dependence or the absolute values. The discrepancy between data and theoretical predictions indicates that the current understanding of initial conditions in models of heavy-ion collisions needs to be revisited to further constrain η/s(T). The measurement of SC(m,n) and NSC(m,n) can providenewconstraintsforthedetailedmodelingoffluctuating initial conditions. The calculations for the two sets of parameters which describe the lower order harmonic correlations best are compared to the data in Fig. 4. As can be seen in Fig. 1 from Ref. [45], for the “param1” parametrization the phase transition from the hadronic to the QGP phase occurs at the lowest temperature, around 150 MeV. This parametrization is also characterized by a moderate slope in η/s(T) which decreases (increases) in the hadronic (QGP) phase. The model calculations in which the temperature of the phase transition is larger than for “param1” are ruled out by the previous measurements [57]. While the correlations between v5and v2are well described at all centralities, the correlations between v5and v3are reproduced in the 0–40% centrality range and deviate by about one σfor 024906-7 S. ACHARYA et al. PHYSICAL REVIEW C 97, 024906 (2018) 0.1− 0.05− 0 6− 10× SC(4,3) (e) 0 0.05 0.1 0.15 6− 10× SC(5,3) (d) 0 0.1 0.2 0.3 6− 10× SC(5,2) (c) 0 2 4 6− 10× SC(4,2) VISH2+1 /s=0.08ηAMPT, /s=0.16ηAMPT, /s=0.08ηMC-KLN, /s=0.2ηMC-KLN, /s=0.08ηMC-Glauber, /s=0.2ηMC-Glauber, (b) 2− 1− 0 6− 10× SC(3,2) = 2.76 TeV NN sPb-Pb c < 5.0 GeV/ T p| < 0.8, 0.2 < η| ALICE (a) 0.3− 0.2− 0.1− 0 NSC ( 4 , 3 ) (E) 0 0.5 1 1.5 NSC ( 5 , 3 ) (D) 0 0.2 0.4 NSC ( 5 , 2 ) (C) 0 0.5 NSC ( 4 , 2 ) (B) 0.1− 0 NSC ( 3 , 2 ) (A) 0 1020304050 10 20304050 Centrality percentile Centrality percentile FIG. 5. The centrality dependence of SC(m,n)andNSC(m,n) in Pb-Pb collisions at √sNN =2.76 TeV. Results are compared to various VISH2+1 calculations [58]. Three initial conditions from AMPT, MC-KLN, and MC-Glauber are drawn as different colors and markers. The η/s parameters are shown as different line styles, the small shear viscosity (η/s =0.08) are shown as solid lines, and large shear viscosities (η/s =0.2 for MC-KLN and MC-Glauber and 0.16 for AMPT) are drawn as dashed lines. Left (right) panels show SC(m,n) (NSC(m,n)). 40–50% centrality. In the case of v4and v3, the same models underestimate the anticorrelation in the data significantly in midcentral collisions and fail similarly for the anticorrelation between v3and v2. The comparison to the VISH2+1 calculation [58]isshown inFig.5. Allcalculations withlargeη/s regardlessof theinitial conditions (η/s =0.2 for MC-KLN and MC-Glauber initial conditions and η/s =0.16 for AMPT initial conditions) fail to describe the centrality dependence of the SC(m,n) observables of all orders, shown in the left panels in Fig. 5. Among the calculations with small η/s (η/s =0.08), the one with the AMPT initial conditions describes the data better than the ones with other initial conditions for all SC(m,n) observables measured, but it cannot describe the data quantitively for most of the centrality ranges. However, NSC(4,2) is sensitive both to the initial conditions and the η/s parametrizations used in the models. Even though NSC(4,2) favors both AMPT initial conditions with η/s = 0.08 and MC-Glauber initial conditions with η/s =0.20, SC(4,2) can only be described by models with smaller η/s. Hence the calculation with large η/s =0.20 is ruled out. We conclude that η/s should be small and that AMPT initial conditionsarefavoredbythedata.TheNSC(5,2)and NSC(5,3) observables are quite sensitive to both the initial conditions and the η/s parametrizations. The SC(4,3) results clearly favor smaller η/s values but NSC(4,3) cannot be described by these models quantitively. The SC(m,n) and NSC(m,n) observables calculated from AMPT simulations are compared with data in Fig. 6.For SC(3,2), the calculation with the default AMPT settings is closest to the data, but none of the AMPT configurations can describe the data fully. The third version based on the string melting configuration without the hadronic rescattering phase is also shown. The hadronic rescattering stage makes both SC(3,2) and NSC(3,2) smaller in the string melting AMPT model but not enough to describe the data. Further investigations proved why the default AMPT model can describe NSC(3,2) but underestimates SC(3,2). By taking the differences in the individual flow harmonics (v2and v3) between the model and data into account, it was possible to recover the difference in SC(3,2) between the data and the model. The discrepancy in SC(3,2) can be explained by the overestimated individual vnvalues as reported in Ref. [100]in all centrality ranges. InthecaseofSC(4,2),thestringmeltingconfigurationofthe AMPTmodelcan describethe datafairly wellwhile thedefault configuration underestimates it. The NSC(4,2) observable is slightly overestimated by the string melting setting which can describe SC(4,2) but the default AMPT configuration can describethe databetter. Theinfluenceofthehadronic rescattering 024906-8 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 0.05 0.1 0.15 0.2 2 v |>1ηΔALICE (PRL.116.132302) | EKRT+Viscous Hydrodynamics /s=0.2)ηparam0 ( /s(T))ηparam1 ( /s=0.08ηVISH2+1, AMPT, AMPT, string melting = 2.76 TeVsPb-Pb c < 5.0 GeV/ p| < 0.8, 0.2 < η| (a) 0 102030405060 Centrality percentile 0.2− 0 0.2 (Theory-Data)/Data 0.02 0.04 0.06 3 v |>1ηΔALICE (PRL.116.132302) | EKRT+Viscous Hydrodynamics /s=0.2)ηparam0 ( /s(T))ηparam1 ( /s=0.08ηVISH2+1, AMPT, AMPT, string melting = 2.76 TeVsPb-Pb (b) 0 102030405060 Centrality percentile 0.2− 0 0.2 (Theory-Data)/Data 0.01 0.02 0.03 4 v |>1ηΔALICE (PRL.116.132302) | EKRT+Viscous Hydrodynamics /s=0.2)ηparam0 ( /s(T))ηparam1 ( /s=0.08ηVISH2+1, AMPT, AMPT, string melting = 2.76 TeVsPb-Pb (c) 0 102030405060 Centrality percentile 0.2− 0 0.2 (Theory-Data)/Data FIG. 13. The individual flow harmonics vnfor n=2−4 in Pb-Pb collisions at √sNN =2.76 TeV [11]. 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Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2Benemérita Universidad Autónoma de Puebla, Puebla, Mexico 3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India 5Budker Institute for Nuclear Physics, Novosibirsk, Russia 6California Polytechnic State University, San Luis Obispo, California, USA 7Central China Normal University, Wuhan, China 8Centre de Calcul de l’IN2P3, Villeurbanne, Lyon, France 9Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 10Centro de Investigación y de Estudios Avanzados (CINVESTAV), Mexico City and Mérida, Mexico 11Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi,” Rome, Italy 12Chicago State University, Chicago, Illinois, USA 13China Institute of Atomic Energy, Beijing, China 14COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan 15Department of Physics, Aligarh Muslim University, Aligarh, India 16Department of Physics, Ohio State University, Columbus, Ohio, USA 17Department of Physics, Pusan National University, Pusan, Republic of Korea 18Department of Physics, Sejong University, Seoul, Republic of Korea 19Department of Physics, University of Oslo, Oslo, Norway 20Department of Physics and Technology, University of Bergen, Bergen, Norway 21Dipartimento di Fisica dell’Università ’La Sapienza’ and Sezione INFN, Rome, Italy 22Dipartimento di Fisica dell’Università and Sezione INFN, Cagliari, Italy 23Dipartimento di Fisica dell’Università and Sezione INFN, Trieste, Italy 24Dipartimento di Fisica dell’Università and Sezione INFN, Turin, Italy 25Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Bologna, Italy 26Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Catania, Italy 27Dipartimento di Fisica e Astronomia dell’Università and Sezione INFN, Padova, Italy 024906-20 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 28Dipartimento di Fisica ‘E.R. Caianiello’ dell’Università and Gruppo Collegato INFN, Salerno, Italy 29Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 30Dipartimento di Scienze e Innovazione Tecnologica dell’Università del Piemonte Orientale and INFN Sezione di Torino, Alessandria, Italy 31Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 32Division of Experimental High Energy Physics, University of Lund, Lund, Sweden 33European Organization for Nuclear Research (CERN), Geneva, Switzerland 34Excellence Cluster Universe, Technische Universität München, Munich, Germany 35Faculty of Engineering, Bergen University College, Bergen, Norway 36Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 37Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 38Faculty of Science, P.J. Šafárik University, Košice, Slovakia 39Faculty of Technology, Buskerud and Vestfold University College, Tonsberg, Norway 40Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 41Gangneung-Wonju National University, Gangneung, Republic of Korea 42Gauhati University, Department of Physics, Guwahati, India 43Helmholtz-Institut für Strahlen- und Kernphysik, Rheinische Friedrich-Wilhelms-Universität Bonn, Bonn, Germany 44Helsinki Institute of Physics (HIP), Helsinki, Finland 45Hiroshima University, Hiroshima, Japan 46Indian Institute of Technology Bombay (IIT), Mumbai, India 47Indian Institute of Technology Indore, Indore, India 48Indonesian Institute of Sciences, Jakarta, Indonesia 49INFN, Laboratori Nazionali di Frascati, Frascati, Italy 50INFN, Laboratori Nazionali di Legnaro, Legnaro, Italy 51INFN, Sezione di Bari, Bari, Italy 52INFN, Sezione di Bologna, Bologna, Italy 53INFN, Sezione di Cagliari, Cagliari, Italy 54INFN, Sezione di Catania, Catania, Italy 55INFN, Sezione di Padova, Padova, Italy 56INFN, Sezione di Roma, Rome, Italy 57INFN, Sezione di Torino, Turin, Italy 58INFN, Sezione di Trieste, Trieste, Italy 59Inha University, Incheon, Republic of Korea 60Institut de Physique Nucléaire d’Orsay (IPNO), Université Paris-Sud, CNRS-IN2P3, Orsay, France 61Institute for Nuclear Research, Academy of Sciences, Moscow, Russia 62Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands 63Institute for Theoretical and Experimental Physics, Moscow, Russia 64Institute of Experimental Physics, Slovak Academy of Sciences, Košice, Slovakia 65Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic 66Institute of Physics, Bhubaneswar, India 67Institute of Space Science (ISS), Bucharest, Romania 68Institut für Informatik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 69Institut für Kernphysik, Johann Wolfgang Goethe-Universität Frankfurt, Frankfurt, Germany 70Institut für Kernphysik, Westfälische Wilhelms-Universität Münster, Münster, Germany 71Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Mexico City, Mexico 72Instituto de Física, Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, Brazil 73Instituto de Física, Universidad Nacional Autónoma de México, Mexico City, Mexico 74IRFU, CEA, Université Paris-Saclay, Saclay, France 75iThemba LABS, National Research Foundation, Somerset West, South Africa 76Joint Institute for Nuclear Research (JINR), Dubna, Russia 77Konkuk University, Seoul, Republic of Korea 78Korea Institute of Science and Technology Information, Daejeon, Republic of Korea 79KTO Karatay University, Konya, Turkey 80Laboratoire de Physique Subatomique et de Cosmologie, Université Grenoble-Alpes, CNRS-IN2P3, Grenoble, France 81Lawrence Berkeley National Laboratory, Berkeley, California, USA 82Moscow Engineering Physics Institute, Moscow, Russia 83Nagasaki Institute of Applied Science, Nagasaki, Japan 024906-21 S. ACHARYA et al. PHYSICAL REVIEW C 97, 024906 (2018) 84National and Kapodistrian University of Athens, Physics Department, Athens, Greece 85National Centre for Nuclear Studies, Warsaw, Poland 86National Institute for Physics and Nuclear Engineering, Bucharest, Romania 87National Institute of Science Education and Research, HBNI, Jatni, India 88National Nuclear Research Center, Baku, Azerbaijan 89National Research Centre Kurchatov Institute, Moscow, Russia 90Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark 91Nikhef, Nationaal instituut voor subatomaire fysica, Amsterdam, Netherlands 92Nuclear Physics Group, STFC Daresbury Laboratory, Daresbury, United Kingdom 93Nuclear Physics Institute, Academy of Sciences of the Czech Republic, ˇ Rež u Prahy, Czech Republic 94Oak Ridge National Laboratory, Oak Ridge, Tennessee, USA 95Petersburg Nuclear Physics Institute, Gatchina, Russia 96Physics Department, Creighton University, Omaha, Nebraska, USA 97Physics department, Faculty of science, University of Zagreb, Zagreb, Croatia 98Physics Department, Panjab University, Chandigarh, India 99Physics Department, University of Cape Town, Cape Town, South Africa 100Physics Department, University of Jammu, Jammu, India 101Physics Department, University of Rajasthan, Jaipur, India 102Physikalisches Institut, Eberhard Karls Universität Tübingen, Tübingen, Germany 103Physikalisches Institut, Ruprecht-Karls-Universität Heidelberg, Heidelberg, Germany 104Physik Department, Technische Universität München, Munich, Germany 105Purdue University, West Lafayette, Indiana, USA 106Research Division and ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt, Germany 107Rudjer Boškovi´c Institute, Zagreb, Croatia 108Russian Federal Nuclear Center (VNIIEF), Sarov, Russia 109Saha Institute of Nuclear Physics, Kolkata, India 110School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom 111Sección Física, Departamento de Ciencias, Pontificia Universidad Católica del Perú, Lima, Peru 112SSC IHEP of NRC Kurchatov Institute, Protvino, Russia 113Stefan Meyer Institut für Subatomare Physik (SMI), Vienna, Austria 114SUBATECH, IMT Atlantique, Université de Nantes, CNRS-IN2P3, Nantes, France 115Suranaree University of Technology, Nakhon Ratchasima, Thailand 116Technical University of Košice, Košice, Slovakia 117Technical University of Split FESB, Split, Croatia 118The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland 119The University of Texas at Austin, Physics Department, Austin, Texas, USA 120Universidad Autónoma de Sinaloa, Culiacán, Mexico 121Universidade de São Paulo (USP), São Paulo, Brazil 122Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil 123Universidade Federal do ABC, Santo Andre, Brazil 124University of Houston, Houston, Texas, USA 125University of Jyväskylä, Jyväskylä, Finland 126University of Liverpool, Liverpool, United Kingdom 127University of Tennessee, Knoxville, Tennessee, USA 128University of the Witwatersrand, Johannesburg, South Africa 129University of Tokyo, Tokyo, Japan 130University of Tsukuba, Tsukuba, Japan 131Université Clermont Auvergne, CNRS/IN2P3, LPC, Clermont-Ferrand, France 132Université de Lyon, Université Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, Lyon, France 133Université de Strasbourg, CNRS, IPHC UMR 7178, F-67000 Strasbourg, France, Strasbourg, France 134Università degli Studi di Pavia, Pavia, Italy 135Università di Brescia, Brescia, Italy 136V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia 137Variable Energy Cyclotron Centre, Kolkata, India 138Warsaw University of Technology, Warsaw, Poland 139Wayne State University, Detroit, Michigan, USA 140Wigner Research Centre for Physics, Hungarian Academy of Sciences, Budapest, Hungary 141Yale University, New Haven, Connecticut, USA 024906-22 SYSTEMATIC STUDIES OF CORRELATIONS BETWEEN … PHYSICAL REVIEW C 97, 024906 (2018) 142Yonsei University, Seoul, Republic of Korea 143Zentrum für Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany aDipartimento DET del Politecnico di Torino, Turin, Italy. bGeorgia State University, Atlanta, Georgia, USA. cM.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia. dDepartment of Applied Physics, Aligarh Muslim University, Aligarh, India. eDeceased. fInstitute of Theoretical Physics, University of Wroclaw, Poland. 024906-23