Observation of flow angle and flow magnitude fluctuations in Pb-Pb collisions at √sNN = 5.02 TeV at the CERN Large Hadron Collider

This is a self-archived version of an original article. This version may differ from the original in pagination and typographic details. Author(s): Title: Year: Version: Copyright: Rights: Rights url: Please cite the original version: CC BY 4.0 https://creativecommons.org/licenses/by/4.0/ Observation of flow angle and flow magnitude fluctuations in Pb-Pb collisions at √sNN = 5.02 TeV at the CERN Large Hadron Collider © 2023 CERN Published version ALICE Collaboration ALICE Collaboration. (2023). Observation of flow angle and flow magnitude fluctuations in Pb-Pb collisions at √sNN = 5.02 TeV at the CERN Large Hadron Collider. Physical Review C, 107, Article L051901. https://doi.org/10.1103/PhysRevC.107.L051901 2023 PHYSICAL REVIEW C 107, L051901 (2023) Letter Observation of flow angle and flow magnitude fluctuations in Pb-Pb collisions at √sNN =5.02 TeV at the CERN Large Hadron Collider S. Acharya et al.∗ (ALICE Collaboration) (Received 28 June 2022; revised 13 February 2023; accepted 20 March 2023; published 24 May 2023) This Letter reports on the first measurements of transverse momentum dependent flow angle nand flow magnitude vnfluctuations determined using new four-particle correlators. The measurements are performed for various centralities in Pb–Pb collisions at a center-of-mass energy per nucleon pair of √sNN =5.02 TeV with ALICE at the CERN Large Hadron Collider. Both flow angle and flow magnitude fluctuations are observed in the presented centrality ranges and are strongest in the most central collisions and for a transverse momentum pT>2 GeV/c. Comparison with theoretical models, including iEBE-VISHNU, MUSIC, and AMPT, show that the measurements exhibit unique sensitivities to the initial state of heavy-ion collisions. DOI: 10.1103/PhysRevC.107.L051901 In ultrarelativistic collisions of heavy ions, such as those at the BNL Relativistic Heavy-Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC), a deconfined state of strongly interacting matter, commonly referred to as quarkgluon plasma (QGP), is predicted to be created under extreme conditions of temperature and energy densities [1,2]. Many experimental results indicate that a strongly coupled QGP is formed in heavy-ion collisions [3–7]. Initial anisotropies of the geometric overlap of the colliding nuclei and spatial inhomogeneities in the energy density drive the collective expansion of the QGP and are transformed through the evolution of the QGP into a momentum anisotropy in the final state [8–10]. This momentum anisotropy is characterized by a Fourier expansion of the distribution of the azimuthal angle, ϕ, of emitted particles [11] d2N dpTdϕ=dN 2πdpT1+2∞  n=1 vn(pT) cos[n(ϕ−n(pT))], (1) where vn(pT) and n(pT) correspond to the magnitude and angle, respectively, of the nth-order harmonic flow vector  Vn(pT)=vn(pT)einn(pT). Here, the transverse momentum, pT, dependence of both the flow magnitude and flow angle has been made explicit. The flow vector quantifies the orientation and magnitude of the anisotropic flow, and the flow angle n is the angle of the symmetry plane of the nth-order flow vector. Typically, the largest flow coefficient is the elliptic flow v2, since it is largely determined by the geometrical overlap of ∗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. the colliding nuclei. However, fluctuations in the position of the colliding nuclei and in the position of nucleons within the nuclei can induce more complex geometrical shapes, which will give rise to nonzero flow coefficients with n>2[12–15], such as the triangular flow v3. Both elliptic and triangular flow coefficients have been measured extensively at RHIC [16–19] and the LHC [20–31]. The comparison to hydrodynamical calculations can constrain the initial conditions of the heavy-ion collisions and the transport properties of the QGP, such as the specific shear viscosity η/s. These comparisons indicate that the system behaves as a strongly coupled low-viscosity fluid [10,32–35]. Fluctuations of the flow angle nand the flow magnitude vnhave been shown to be present in hydrodynamical models [36,37]. These fluctuations are possibly due to thermal hydrodynamic fluctuations during the QGP evolution [38]. The flow angle fluctuations (FAF) are the fluctuations of n(pT) determined by a subset of particles at a specific pTwith respect to the symmetry plane determined by the total set of particles, n. If such fluctuations are present, n(pT)= n. The flow magnitude fluctuations (FMF)ofthevnat different pTcan be understood as a decorrelation where vn(pT)vn = v2 n(pT)v2 n. The determination of QGP properties, such as η/s,relyon the comparison of theoretical model calculations to experimental data. In order to provide an unbiased extraction of the QGP properties, the models should account for the fluctuations in the flow angle and flow magnitude. Measurements at the LHC have reported the existence of pT-dependent flow vector fluctuations [39–42]. However, those measurements rely on observables constructed from two-particle correlations, which intrinsically contain contributions from both the FAF and FMF with no way to separate the two experimentally. In this Letter the FAF and FMF are measured with two new four-particle correlation functions to separate the components of the pT-dependent fluctuations of the flow vector. 2469-9985/2023/107(5)/L051901(13) L051901-1 ©2023 CERN, for the ALICE Collaboration S. ACHARYA et al. PHYSICAL REVIEW C 107, L051901 (2023) The FAF is quantified by Af n=cos nϕPOI 1+ϕPOI 2−ϕ3−ϕ4 cos nϕPOI 1+ϕ2−ϕPOI 3−ϕ4=v2 n(pT)v2 ncos 2n[n(pT)−n] v2 n(pT)v2 n ≃cos 2n[n(pT)−n]w,(2) where the POI superscript refers to particles of interest selected from a narrow transverse momentum range and the wsubscript means that Af nis averaged over the event ensemble with each event having a weight equal to the fourth power of vn[43]. The double brackets refer to an average over all particles and all events, and the single brackets refer to an average over all events. A value of Af n<1 indicates the presence of pT-dependent FAF. A large deviation from unity suggests that the symmetry plane at a specific pPOI Tdeviates from the common symmetry plane. The FMF are studied with Mf n=cos nϕPOI 1+ϕ2−ϕPOI 3−ϕ4cos nϕPOI 1−ϕa 3cos n[ϕ2−ϕ4] cos n[ϕ1+ϕ2−ϕ3−ϕ4]/cos n[ϕ1−ϕ2]2=v2 n(pT)v2 nv2 n(pT)v2 n v4 nv2 n2.(3) A deviation of Mf nfrom unity indicates the presence of pT-dependent FMF. The magnitude of the deviation will show how strongly the flow magnitude in a specific pTrange, vn(pT), is decorrelated with respect to the integrated flow, vn. The correlators Af nand Mf nprobe higher moments of the distribution of flow fluctuations compared to correlators traditionally used previously with two-particle techniques [39–41]. The lower-order moments of the FAF and FMF cannot be measured separately in experiments [36,44] but can be approximated by constructing the lower and upper limits of the first moment of flow angle and magnitude fluctuations, respectively. The lower limit of the first-moment FAF cos n[n(pT)−n]is calculated with a double angle formula as Af n+1 2⩾cos n[n(pT)−n].(4) The flow vector fluctuations are calculated as the ratio of the pT-differential flow coefficient, defined as vn{2}=cos nϕPOI 1−ϕ2 cos n[ϕ1−ϕ2] =vn(pT)vncos n[n(pT)−n] v2 n (5) and the pT-integrated flow coefficient in a narrow pTinterval [36], i.e., vn[2] =cos nϕPOI 1−ϕPOI 2=v2 n(pT).(6) The flow vector fluctuations is then given by vn{2}/vn[2] =vn(pT)vncos n[n(pT)−n] v2 n(pT)v2 n ,(7) which satisfies the Cauchy-Schwartz inequality for two observables Xand Y,XY⩽X2Y2, as cos n(n(pT)− n)⩽1. The ratio of Eqs. (4) and (7) determines the upper limit of the first-order FMF vn{2}/vn[2] Af n+12 ⩽vn(pT)vn v2 n(pT)v2 n .(8) The limits on the first-moment flow angle and magnitude fluctuations connect the study of the separated fluctuations with prior studies of flow vector fluctuations based on twoparticle correlations [39–41]. All the above correlators are calculated with the generic framework [45,46], which corrects the nonuniformities in the acceptance of the detector. The statistical uncertainties of these two correlators in Eqs. (2) and (3) are estimated with the bootstrap method of random sampling with replacement. The correlators Af 2and Mf 2are measured based on 5.4× 107Pb–Pb collisions recorded with the ALICE experiment [47] in 2015 at a center-of-mass energy per nucleon pair of √sNN =5.02 TeV. Experimentally, events are selected based on a minimum bias trigger achieved by requiring a coincidence of signals in the two V0 scintillator arrays, V0A with a pseudorapidity range 2.8<η<5.1, and V0C with a pseudorapidity range −3.7<η<−1.7. Additionally, a reconstructed primary vertex within ±10 cm of the nominal interaction point along the beam axis is required. Events with significant pileup from out-of-bunch collisions within the time projection chamber (TPC) readout time will have incorrect multiplicity and cannot be used to assess the collision properties of a given centrality class. Such pileup events are rejected based on cuts of the correlation between the number of tracks measured with different detectors. A variation of the criteria for pileup rejection is considered for the systematic uncertainties [48]. The centrality of the events is measured using information from the V0A and V0C detectors [49]. Charged particle tracks, hereafter simply called tracks, are reconstructed using the inner tracking system (ITS) [50] and the TPC [51]. Tracks are selected with at least 70 TPC space points out of 159 points and a χ2per TPC cluster less than 4[52]. To reduce contamination from secondary particles, tracks are selected with a distance of closest approach to the primary vertex of less than 2 cm in the longitudinal direction and a pT-dependent selection ranging from 0.2 cm at pT= 0.2 GeV/cto 0.016 cm at pT=5GeV/cin the transverse L051901-2 OBSERVATION OF FLOW ANGLE AND FLOW MAGNITUDE … PHYSICAL REVIEW C 107, L051901 (2023) direction. Tracks are selected within the full TPC and ITS acceptance of |η|<0.8. Additionally, as the regime of hard processes is not of interest in this work, the kinematic range of the tracks is restricted to 0.2<pT<5GeV/c, where most of the tracks originate from the thermalized medium. In order to suppress nonflow correlation contributions, such as resonance decays and jets, which are not related to collective behavior, the subevent method is utilized to calculate the correlators. In this method the event is divided into subevents separated by a gap in pseudorapidity denoted |η|. This ensures that short-range nonflow correlations between particles from the same subevent, mostly originating from resonances, are not introduced. An ηgap of |η|>0.8 is used for two-particle correlations and |η|>0 for four-particle correlations in order to ensure optimal balance between the statistical precision and nonflow suppression. To further investigate the nonflow suppression, the analysis is also performed with the so-called like-sign method, where only positively or negatively charged particle tracks are considered for analysis. The difference is less than 1% compared to the measurements of Af 2and Mf 2using all tracks. Furthermore, the analysis is repeated with increasing pseudorapidity gaps between the subevents. Pseudorapidity gaps of |η|>0, |η|>0.4, and η|>0.8 are tested, and it is found that the measurements of Af 2and Mf 2differ by less than 1%, when measured with different pseudorapidity gaps. Additional Monte Carlo studies using HIJING [53], a model that does not feature collective effects, but involves particle correlations arising from other sources, indicate that nonflow is sufficiently suppressed with the applied pseudorapidity gaps. The HIJING calculations of the four-particle correlation functions defined in Eqs. (2) and (3) show no statistically significant difference from zero. Based on the model studies, the like-sign method, and the variations of the pseudorapidity gaps, the nonflow correlation contributions are less than 1% of the measured values of Af 2and Mf 2. Systematic uncertainties are evaluated by varying the event and track selection criteria. The systematic uncertainty is presented for Af 2, as the uncertainties are of a similar size for both observables. Since the systematic uncertainty may depend on the collision centrality and the pTbin, only the largest contribution from each source is mentioned below. The systematic uncertainty associated with the event selection criteria is evaluated by varying the selection on the vertex position along the beam direction (from 10 cm to 7, 8, or 9 cm), the magnetic field polarity, and the criteria for rejecting pileup events, and is below 1%. The robustness of the centrality determination is investigated by repeating the analysis using the centrality estimated at midrapidity from hits in the silicon pixel detector (SPD) instead of the V0, resulting in a negligible difference. Uncertainties related to track selection are estimated by considering different track reconstructions and track quality selection criteria. Changing the track reconstruction to include tracks without hits in the SPD leads to a variation of, at most, 1.7%. The quality of the reconstructed tracks is varied by changing the minimum number of TPC space points to 80 and 90, which leads to a difference of 1.5% on the measured correlators. Uncertainties related to the variations in the distance of closest approach in both longitudinal and transverse directions are negligible, indicating that the effect of contaminations from secondary particles on the measurements is insignificant. Finally, tightening the χ2per number of TPC clusters from 4 to 2.5 gives an uncertainty of, at most, 3%. The total systematic uncertainty is calculated as the quadratic sum of the individual sources that have a statistically significant contribution according to a statistical test [54]. Measured values of Af 2are present in Fig. 1as a function of the transverse momentum pTin selected collision centrality classes. The results are presented from 0.2 GeV/cup to 4GeV/csince the requirement of two particles at high pTfor the four-particle correlations limits the available data sample. In the 0–5 % most central collisions, finite and increasing large deviations from unity are observed starting from pT≈ 2.5 GeV/c. As previously mentioned, this deviation cannot be attributed to nonflow effects, whose contributions are negligible. With more than 5σsignificance of the deviation at pT>3GeV/cacross the presented centralities, these measurements provide the first observation of pT-dependent FAF. In centralities 10–20 % and 30–40 %, the fluctuation weakens in comparison to 0–5 % most central collisions and reaches around 5–7 % deviation from unity at 3 <pT<4GeV/c. The increasing deviation from unity with pT>2.5GeV/c observed in data suggests that the elliptic flow at large transverse momentum (pT>2.5GeV/c) may not be correlated with the reference flow and a common symmetry plane. This will affect the comparison of measurements relying on a common symmetry plane between particles at high and low pTwith theoretical models that do not feature FAF. Theoretical calculations with AMPT [57,58], MUSIC [59,60], and iEBE-VISHNU [61] models are, when available, compared to the data in Fig. 1. The AMPT transport model uses partonic interactions within the string melting tune, while a quark coalescence model is utilized to form hadrons, which are then transported through a hadronic cascade model [62]. The input parameters of the AMPT model are tuned to measurements of dN/dη,pT,spectra, and elliptic flow of charged pions, kaons, and protons from ALICE [57,63]. On the other hand, the MUSIC model is an event-by-event (3+1D) viscous hydrodynamic model and is used with both Glauber [64] and TRENTo [65] initial conditions. Different values of η/sof 0.08, 0.12, and 0.16 are used with TRENTo initial conditions [56]. Finally, the iEBE-VISHNU model is an event-byevent (2+1)D viscous hydrodynamical model coupled to the hadronic cascade model UrQMD [66]. This model has been successful in describing collective phenomena, as well as event-by-event fluctuations, in several collision systems and energies [55,67]. The iEBE-VISHNU model calculations with TRENTo initial conditions and a temperature-dependent specific shear viscosity η/s(T)[68] are also shown. The iEBEVISHNU model calculations are available at pTranges below 3GeV/c. The AMPT calculation presented here describes the data well in the 0–5 % most central collisions and captures the deviation from unity in the highest pTbin. At higher centralities, the AMPT calculation overestimates the deviation from unity at high pT. The comparison of the MUSIC calculations with Glauber and TRENTo initial conditions L051901-3 S. ACHARYA et al. PHYSICAL REVIEW C 107, L051901 (2023) 0.5 1 1.5 2 2.5 3 3.5 4 )c (GeV/ T p 0.8 1 2 f A 5%−0 ALICE = 5.02 TeV NN sPb−Pb 0.5 1 1.5 2 2.5 3 3.5 4 )c (GeV/ T p 0.8 1 2 f A 20%−10 c < 5 GeV/ ref T p0.2 < ALICE AMPT 0.5 1 1.5 2 2.5 3 3.5 4 )c (GeV/ T p 0.9 1 2 f A 40%−30 /s = 0.08ηGLAUBER+MUSIC, /s = 0.08ηTRENTo+MUSIC, /s = 0.12ηTRENTo+MUSIC, /s = 0.16ηTRENTo+MUSIC, /s(T)ηTRENTo+iEBE-VISHNU, FIG. 1. The flow angle fluctuation Af 2in Pb–Pb collisions at √sNN =5.02 TeV as a function of the transverse momentum, pT, in centrality classes 0–5 % (left), 10–20 % (middle), and 30–40 % (right). Comparison with iEBE-VISHNU with TRENTo initial conditions and η/s(T) [55], MUSIC with Glauber initial conditions and η/s=0.08 [56], MUSIC with TRENTo initial conditions and η/s=0.08,0.12,0.16 [56], and AMPT [57] are shown as colored bands. shows that Af 2is sensitive to the fluctuations in the initial state with little to no sensitivity to the different values of specific shear viscosity. This observation is consistent with the AMPT calculations presented in [69], where AMPT with different values of specific shear viscosity and initial conditions are compared. The iEBE-VISHNU calculation underestimates the deviation of Af 2from unity at pT>2.5GeV/cacross the presented centralities with the largest difference in the 0– 5 % most central collisions. The iEBE-VISHNU model with TRENTo initial conditions uses parameters extracted from a Bayesian analysis [68] in contrast to the MUSIC models, which use standard TRENTo initial conditions with p=0 [65]. The extracted parameters from the Bayesian analysis represent the current best understanding of the initial conditions and QGP transport properties. Including additional constraints in the Bayesian analyses, such as Af 2, should improve our understanding of the event-by-event fluctuating initial state thus allowing for a more robust and unbiased extraction of the expansion properties of the matter formed in these collisions. The measurements of the pT-dependent FMF, Mf 2in centrality classes 0–5 %, 10–20 %, and 30– 40 % are shown in Fig. 2. A substantial deviation of Mf 2 from unity is observed in the 0–5 % most central collisions. This deviation by more than 5σsignificance at pT> 3GeV/cconstitutes the first observation of pT-dependent FMF. The measurements show that the pT-differential flow coefficients decorrelate with the pT-integrated flow coefficient as the transverse momentum increases. In centrality 0–5 %, where the initial state fluctuations are most significant, the flow magnitude deviates from unity for pTabove 2GeV/c. Deviations increase with rising pTand are more pronounced in the 0–5 % central collisions compared to those observed in the 10–20 % and 30–40 % centrality ranges. Mf 2is not restricted to be below unity as seen in Fig. 2at 30–40 % centrality. The observable Mf nis not constructed to satisfy the Cauchy-Schwarz inequality as such an observable, v2 n(pT)v2 n/v4 n(pT)v4 n, would require four particles from a narrow pTrange. The flow vector fluctuations measured with two-particle correlations and the FAF measured with Af 2, however, can only be larger than unity due to nonflow effects 0.5 1 1.5 2 2.5 3 3.5 )c (GeV/ T p 0.8 0.9 1 1.1 2 f M 5%−0 ALICE = 5.02 TeV NN sPb−Pb 0.5 1 1.5 2 2.5 3 3.5 )c (GeV/ T p 0.8 0.9 1 1.1 2 f M 20%−10 c < 5 GeV/ ref T p0.2 < ALICE AMPT 0.5 1 1.5 2 2.5 3 3.5 4 )c (GeV/ T p 0.8 0.9 1 1.1 2 f M 40%−30 /s = 0.08ηGLAUBER+MUSIC, /s = 0.08ηTRENTo+MUSIC, /s = 0.12ηTRENTo+MUSIC, /s = 0.16ηTRENTo+MUSIC, /s(T)ηTRENTo+iEBE-VISHNU, FIG. 2. The flow magnitude fluctuation Mf 2in Pb–Pb collisions at √sNN =5.02 TeV as a function of the transverse momentum, pT,in centrality classes 0–5 % (left), 10–20 % (middle), and 30–40 % (right). Comparison with iEBE-VISHNU with TRENTo initial conditions and η/s(T)[55], MUSIC with Glauber initial conditions and η/s=0.08 [56], MUSIC with TRENTo initial conditions and η/s=0.08,0.12,0.16 [56], and AMPT [57] are shown as colored bands. L051901-4 OBSERVATION OF FLOW ANGLE AND FLOW MAGNITUDE … PHYSICAL REVIEW C 107, L051901 (2023) [37]. The nonflow studies mentioned previously show that nonflow correlations are negligible for Mf 2, so the deviation from unity must be due to the FMF. The AMPT transport model calculation succeeds in describing the FMF in the most central collisions, where it also describes the FAF (Fig. 1left). At higher centralities, the AMPT model significantly overestimates the data even at low pT, but it qualitatively captures the increasing trend of Mf 2in the 30–40 % centrality interval. The AMPT model works well in qualitatively describing both FAF and FMF without a hydrodynamic phase. This is possibly due to the fact that these effects mainly originate in the initial state. The MUSIC models show strong sensitivity to the η/sin 0–5 % most central collisions as well as a sensitivity to the different initial conditions. The dependence on η/sis unexpected and in contrast to the findings in [69], where the magnitude of the flow fluctuations is found to be independent of the value of η/s. In the 10–20 % and 30–40 % centrality intervals, Mf 2shows no sensitivity to η/sbut is still affected by the different initial conditions. The MUSIC models overestimate the deviation of Mf 2from unity in all presented centrality classes. The iEBE-VISHNU calculations underestimate the effect in 0–5 % centrality showing almost no pTdependence. In the 10–20 % and 30–40 % centrality intervals, the model captures the increasing trend with pTand, consequently, describes the data. The comparison of the measurements with the above models confirms that the FMF are driven by initial state fluctuations in noncentral collisions. However, the dependence of Mf 2on η/sin the 0-5 % central collisions with the MUSIC model is not well understood. The large discrepancy between the iEBE-VISHNU model and the data in central collisions suggests that the FMF could be an important observable in Bayesian analyses and could contribute further improvements of the extracted parameters used in the stateof-the-art description of the initial state and the QGP transport properties. Equations (4) and (8) allow for the determination of the lower and upper limit for the contribution of the FAF and FMF, respectively, to the flow vector fluctuations defined in Eq. (7). Thus the lower moments of the FAF and FMF, which cannot be directly accessed in experiments, can be explored. The lower limit on the first-order FAF, the upper limit on the first-order FMF, and the total flow vector fluctuations are shown as a function of centrality for the 3 <pT<4GeV/c range in Fig. 3. In central collisions, the upper limit on the FMF is higher than the lower limit of the FAF up to 10% centrality. For the 10–30 % centrality interval, the limits are similar, and above 30% centrality, the flow magnitude upper limits are much smaller, and the FAF dominate the overall flow vector fluctuations completely. This is consistent with the measurements shown in Figs. 1and 2, where Mf 2approaches unity faster with increasing centrality than Af 2and even goes above unity in semicentral collisions. While pTdependent FAF and FMF are both present in central Pb–Pb collisions, the effects of FAF are present in all centralities considered in this work compared to the much smaller FMF in noncentral collisions. The AMPT transport model calculations overestimate the flow vector fluctuations v2{2}/v2[2] 0 0.05 0.1 0.15 0.2 Absolute contribution c < 4 GeV/ T p3 < ALICE = 5.02 TeV NN sPb−Pb min 〉] 2 Ψ)- T p( 2 Ψcos 2[〈 max 1/2 )〉 2 2 v〈〉) T p( 2 2 v〈/(〉 2 v) T p( 2 v〈 [2] 2 v/{2} 2 v Data AMPT 0 5 10 15 20 25 30 35 40 Centrality (%) 0 0.2 0.4 0.6 0.8 1 1.2 Relative contribution FIG. 3. The lower limit of the first-order flow angle fluctuations, upper limit of the first-order flow magnitude fluctuations, and the flow vector fluctuations as a function of centrality for the 3.0< pT<4.0 GeV/c. The lower and upper limits are denoted by the arrows. The top panel shows the absolute contribution and the bottom panel the contribution relative to the overall flow vector fluctuations. Comparisons to AMPT [57] are shown as colored bands. as well as the limits of the first-order FAF and FMF in the central collisions. At higher centralities, AMPT describes the lower and upper limits well, whereas the flow vector fluctuations are still overestimated by the model, as in central collisions. Hydrodynamic calculations for the limits are not available. In summary, the pT-dependent flow angle fluctuations and flow magnitude fluctuations of the second-order flow vector  V2are measured in Pb–Pb collisions at √sNN =5.02 TeV with the correlators Af 2and Mf 2in centrality intervals 0–5 %, 10–20 %, and 30–40 %. Large deviations from unity of both Af 2(≈20%) and Mf 2(≈10%) are observed at pT>3GeV/c in central collisions, where the event-by-event fluctuations of the position of the colliding nucleons dominate over the geometric response. In semicentral collisions, both flow angle and flow magnitude fluctuations decrease. The flow angle fluctuations reach 5–7 %, and the flow magnitude fluctuations reach around 2% and are above unity in 30–40 % centrality for the presented pTrange. The flow magnitude fluctuations decrease faster than the flow angle fluctuations up to 40% centrality, where the flow vector fluctuations are almost solely due to flow angle fluctuations. The comparison of the measurements to theoretical models shows that the observables are sensitive to the initial conditions of heavy-ion collisions. This suggests that the fluctuations originate during the early stages of the QGP evolution. The observation of flow angle and flow magnitude fluctuations thus gives additional insight into the nature of event-by-event fluctuations in the initial state L051901-5 S. ACHARYA et al. PHYSICAL REVIEW C 107, L051901 (2023) of heavy-ion collisions and can be used to constrain the initial conditions and QGP properties. The ALICE Collaboration would like to thank all its engineers and technicians for their invaluable contributions to the construction of the experiment and the CERN accelerator teams for the outstanding performance of the LHC complex. The ALICE Collaboration gratefully acknowledges the resources and support 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 building and running the ALICE detector: A. I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) 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 Nationalstiftung für Forschung, Technologie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Financiadora de Estudos e Projetos (Finep), Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) and Universidade Federal do Rio Grande do Sul (UFRGS), Brazil; Bulgarian Ministry of Education and Science, within the National Roadmap for Research Infrastructures 2020–2027 (object CERN), Bulgaria; 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 Education and Croatian Science Foundation, Croatia; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research | Natural Sciences, the VILLUM FONDEN and Danish 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 Physique des Particules (IN2P3) and Centre National de la Recherche Scientifique (CNRS), France; Bundesministerium für Bildung und Forschung (BMBF) and GSI Helmholtzzentrum für Schwerionenforschung GmbH, Germany; General Secretariat for Research and Technology, Ministry of Education, Research and Religions, Greece; National Research, Development and Innovation Office, Hungary; Department of Atomic Energy Government of India (DAE), Department of Science and Technology, Government of India (DST), University Grants Commission, Government of India (UGC) and Council of Scientific and Industrial Research (CSIR), India; National Research and Innovation Agency - BRIN, Indonesia; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT) and Japan Society for the Promotion of Science (JSPS) KAKENHI, Japan; Consejo Nacional de Ciencia (CONACYT) y Tecnología, through Fondo de Cooperación Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Academico (DGAPA), Mexico; Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO), Netherlands; The Research Council of Norway, Norway; Commission on Science and Technology for Sustainable Development in the South (COMSATS), Pakistan; Pontificia Universidad Católica del Perú, Peru; Ministry of Education and Science, National Science Centre and WUT ID-UB, Poland; Korea Institute of Science and Technology Information and National Research Foundation of Korea (NRF), Republic of Korea; Ministry of Education and Scientific Research, Institute of Atomic Physics, Ministry of Research and Innovation and Institute of Atomic Physics and University Politehnica of Bucharest, Romania; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, 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 (NSTDA), Thailand Science Research and Innovation (TSRI) and National Science, Research and Innovation Fund (NSRF), Thailand; Turkish Energy, Nuclear and Mineral Research Agency (TENMAK), Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and Technology Facilities Council (STFC), United Kingdom; National Science Foundation of the United States of America (NSF) and United States Department of Energy, Office of Nuclear Physics (DOE NP), United States of America. In addition, individual groups or members have received support from: Marie Skłodowska Curie, European Research Council, Strong 2020 - Horizon 2020 (Grant Nos. 950692, 824093, 896850), European Union; Academy of Finland (Center of Excellence in Quark Matter) (Grants No. 346327 and No. 346328), Finland; Programa de Apoyos para la Superación del Personal Académico, UNAM, Mexico. [1] E. V. Shuryak, Quark-gluon plasma and hadronic production of leptons, photons and psions, Phys. Lett. B 78, 150 (1978). [2] E. V. Shuryak, Quantum chromodynamics and the theory of superdense matter, Phys. Rep. 61, 71 (1980). [3] I. Arsene et al. (BRAHMS Collaboration), Quark gluon plasma and color glass condensate at RHIC? The perspective from the BRAHMS experiment, Nucl. Phys. A 757, 1 (2005). [4] J. Adams et al. (STAR Collaboration), Experimental and theoretical challenges in the search for the quark gluon plasma: The STAR Collaboration’s critical assessment of the evidence from RHIC collisions, Nucl. Phys. A 757, 102 (2005). [5] K. Adcox et al. (PHENIX Collaboration), Formation of dense partonic matter in relativistic nucleus-nucleus collisions at RHIC: Experimental evaluation by the PHENIX collaboration, Nucl. Phys. A 757, 184 (2005). L051901-6 OBSERVATION OF FLOW ANGLE AND FLOW MAGNITUDE … PHYSICAL REVIEW C 107, L051901 (2023) [6] B. B. Back et al. (PHOBOS Collaboration), The PHOBOS perspective on discoveries at RHIC, Nucl. Phys. A 757,28 (2005). [7] B. Müller, J. Schukraft, and B. Wyslouch, First Results from Pb+Pb collisions at the LHC, Annu. Rev. Nucl. Part. Sci. 62, 361 (2012). [8] J.-Y. Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46, 229 (1992). [9] S. A. Voloshin, A. M. Poskanzer, and R. Snellings, Collective phenomena in non-central nuclear collisions, Landolt-Bornstein 23, 293 (2010). [10] U. Heinz and R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 63, 123 (2013). [11] S. Voloshin and Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions, Z. Phys. C 70, 665 (1996). [12] B. Alver and G. Roland, Collision geometry fluctuations and triangular flow in heavy-ion collisions, Phys. Rev. C 81, 054905 (2010) [82, 039903(E) (2010)]. [13] B. H. Alver, C. Gombeaud, M. Luzum, and J.-Y. Ollitrault, Triangular flow in hydrodynamics and transport theory, Phys. Rev. C 82, 034913 (2010). [14] D. Teaney and L. Yan, Triangularity and dipole asymmetry in heavy ion collisions, Phys. Rev. C 83, 064904 (2011). [15] M. Luzum, Collective flow and long-range correlations in relativistic heavy ion collisions, Phys. Lett. B 696, 499 (2011). [16] K. H. Ackermann et al. (STAR Collaboration), Elliptic Flow in Au + Au Collisions at √sNN =130 GeV, Phys.Rev.Lett.86, 402 (2001). [17] S. S. Adler et al. (PHENIX Collaboration), Elliptic Flow of Identified Hadrons in Au+Au Collisions at √sNN =200-GeV, Phys. Rev. Lett. 91, 182301 (2003). [18] L. Adamczyk et al. (STAR Collaboration), Third harmonic flow of charged particles in Au+Au collisions at √sNN =200 GeV, Phys. Rev. C 88, 014904 (2013). [19] A. Adare et al. (PHENIX Collaboration), Measurements of Elliptic and Triangular Flow in High-Multiplicity 3He +Au Collisions at √sNN =200 GeV, Phys.Rev.Lett.115, 142301 (2015). [20] K. Aamodt et al. (ALICE Collaboration), Elliptic Flow of Charged Particles in Pb-Pb Collisions at 2.76 TeV, Phys. Rev. Lett. 105, 252302 (2010). [21] K. Aamodt et al. (ALICE Collaboration), Higher Harmonic Anisotropic Flow Measurements of Charged Particles in Pb-Pb Collisions at √sNN=2.76 TeV, Phys. Rev. Lett. 107, 032301 (2011). [22] B. Abelev et al. (ALICE Collaboration), Elliptic flow of identified hadrons in Pb-Pb collisions at √sNN =2.76TeV, J. High Energy Phys. 06 (2015) 190. [23] J. Adam et al. (ALICE Collaboration), Anisotropic Flow of Charged Particles in Pb-Pb Collisions at √sNN =5.02 TeV, Phys. Rev. Lett. 116, 132302 (2016). [24] S. Acharya et al. (ALICE Collaboration), Linear and non-linear flow modes in Pb-Pb collisions at √sNN =2.76 TeV, Phys. Lett. B773, 68 (2017). [25] G. Aad et al. (ATLAS Collaboration), Measurement of the azimuthal anisotropy for charged particle production in √sNN = 2.76 TeV lead-lead collisions with the ATLAS detector, Phys. Rev. C 86, 014907 (2012). [26] G. Aad etal. (ATLAS Collaboration), Measurement of the pseudorapidity and transverse momentum dependence of the elliptic flow of charged particles in lead-lead collisions at √sNN = 2.76 TeV with the ATLAS detector, Phys. Lett. B 707, 330 (2012). [27] G. Aad et al. (ATLAS Collaboration), Measurement of the distributions of event-by-event flow harmonics in lead-lead collisions at √sNN =2.76 TeV with the ATLAS detector at the LHC, J. High Energy Phys. 11 (2013) 183. [28] S. Chatrchyan et al. (CMS Collaboration), Centrality dependence of dihadron correlations and azimuthal anisotropy harmonics in PbPb collisions at √sNN =2.76 TeV, Eur. Phys. J. C 72, 10052 (2012). [29] S. Chatrchyan et al. (CMS Collaboration), Measurement of the elliptic anisotropy of charged particles produced in PbPb collisions at √sNN =2.76 TeV, Phys.Rev.C87, 014902 (2013). [30] S. Chatrchyan et al. (CMS Collaboration), Azimuthal Anisotropy of Charged Particles at High Transverse Momenta in PbPb Collisions at √sNN =2.76 TeV, Phys. Rev. Lett. 109, 022301 (2012). [31] S. Acharya et al. (ALICE Collaboration), Anisotropic flow in Xe-Xe collisions at √sNN =5.44 TeV, Phys. Lett. B 784,82 (2018). [32] M. Luzum and H. Petersen, Initial state fluctuations and final state correlations in relativistic heavy-ion collisions, J. Phys. G 41, 063102 (2014). [33] E. Shuryak, Strongly coupled quark-gluon plasma in heavy ion collisions, Rev. Mod. Phys. 89, 035001 (2017) [34] H. Song, Y. Zhou, and K. Gajdosova, Collective flow and hydrodynamics in large and small systems at the LHC, Nucl. Sci. Tech. 28, 99 (2017). [35] (ALICE Collaboration), The ALICE experiment – A journey through QCD, arXiv:2211.04384 [nucl-ex]. [36] U. Heinz, Z. Qiu, and C. Shen, Fluctuating flow angles and anisotropic flow measurements, Phys. Rev. C 87, 034913 (2013). [37] F. G. Gardim, F. Grassi, M. Luzum, and J.-Y. Ollitrault, Breaking of factorization of two-particle correlations in hydrodynamics, Phys.Rev.C87, 031901(R) (2013). [38] A. Sakai, K. Murase, and T. Hirano, Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations, Phys. Rev. C 102, 064903 (2020). [39] S. Acharya et al. (ALICE Collaboration), Searches for transverse momentum dependent flow vector fluctuations in Pb-Pb and p-Pb collisions at the LHC, J. High Energy Phys. 09 (2017) 032. [40] S. Chatrchyan et al. (CMS Collaboration), Studies of azimuthal dihadron correlations in ultra-central PbPb collisions at √sNN =2.76TeV, J. High Energy Phys. 02 088 (2014). [41] V. Khachatryan et al. (CMS Collaboration), Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions, Phys. Rev. C 92, 034911 (2015). [42] K. Aamodt et al. (ALICE Collaboration), Harmonic decomposition of two-particle angular correlations in Pb-Pb collisions at √sNN =2.76 TeV, Phys. Lett. B 708, 249 (2012). [43] P. Bo˙ zek and W. Broniowski, Longitudinal decorrelation measures of flow magnitude and event-plane angles in ultrarelativistic nuclear collisions, Phys. Rev. C 97, 034913 (2018). L051901-7 S. ACHARYA et al. PHYSICAL REVIEW C 107, L051901 (2023) [44] P. Bo˙ zek and R. Samanta, Higher order cumulants of transverse momentum and harmonic flow in relativistic heavy ion collisions, Phys.Rev.C104, 014905 (2021). [45] A. Bilandzic, C. H. Christensen, K. Gulbrandsen, A. Hansen, and Y. Zhou, Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations, Phys. Rev. C 89, 064904 (2014). [46] Z. Moravcova, K. Gulbrandsen, and Y. Zhou, Generic algorithm for multiparticle cumulants of azimuthal correlations in high energy nucleus collisions, Phys. Rev. C 103, 024913 (2021). [47] K. Aamodt et al. (ALICE Collaboration), The ALICE experiment at the CERN LHC, JINST 3, S08002 (2008). [48] B. Abelev et al. (ALICE Collaboration), Performance of the ALICE experiment at the CERN LHC, J. Mod. Phys. A 29, (2014) 1430044. [49] B. Abelev et al. (ALICE Collaboration), Centrality determination of Pb-Pb collisions at √sNN =2.76 TeV with ALICE, Phys. Rev. C 88, 044909 (2013). [50] K. Aamodt et al. (ALICE Collaboration), Alignment of the ALICE Inner Tracking System with cosmic-ray tracks, JINST 5 (2010) P03003. [51] J. Alme et al., The ALICE TPC, a large 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Methods Phys. Res. A 622, 316 (2010). [52] (ALICE Collaboration), The ALICE definition of primary particles, ALICE-PUBLIC-2017-005 (June 2017), https://cds.cern. ch/record/2270008. [53] X.-N. Wang and M. Gyulassy, HIJING: A Monte Carlo model for multiple jet production in pp, pA, and AA collisions, Phys. Rev. D 44, 3501 (1991). [54] R. Barlow, Systematic errors: Facts and fictions, in Conference on Advanced Statistical Techniques in Particle Physics, pp. 134–144, 7, 2002, arXiv:hep-ex/0207026. [55] W. Zhao, H.-j. Xu, and H. Song, Collective flow in 2.76 A TeV and 5.02 A TeV Pb+Pb collisions, Eur.Phys.J.C77, 645 (2017). [56] P. Bozek and R. Samanta, Factorization breaking for higher moments of harmonic flow, Phys.Rev.C105, 034904 (2022). [57] G.-L. Ma and Z.-W. Lin, Predictions for √sNN =5.02 TeV Pb+Pb collisions from a multi-phase transport model, Phys. Rev. C 93, 054911 (2016). [58] Z.-W. Lin, C. M. Ko, B.-A. Li, B. Zhang, and S. Pal, A multiphase transport model for relativistic heavy ion collisions, Phys. Rev. C 72, 064901 (2005). [59] B. Schenke, S. Jeon, and C. Gale, Elliptic and Triangular Flow in Event-by-Event (3+1)D Viscous Hydrodynamics, Phys. Rev. Lett. 106, 042301 (2011). [60] B. Schenke, S. Jeon, and C. Gale, (3+1)D hydrodynamic simulation of relativistic heavy-ion collisions, Phys. Rev. C 82, 014903 (2010). [61] C. Shen, Z. Qiu, H. Song, J. Bernhard, S. Bass, and U. Heinz, The iEBE-VISHNU code package for relativistic heavy-ion collisions, Comput. Phys. Commun. 199, 61 (2016). [62] B.-A. Li and C. M. Ko, Formation of superdense hadronic matter in high-energy heavy ion collisions, Phys. Rev. C 52, 2037 (1995). [63] J. Xu and C. M. Ko, Pb-Pb collisions at √sNN =2.76 TeV in a multiphase transport model, Phys.Rev.C83, 034904 (2011). [64] P. Bo˙ zek, W. Broniowski, M. Rybczynski, and G. Stefanek, GLISSANDO 3: GLauber Initial-State Simulation AND mOre, ver. 3, Comput. Phys. Commun. 245, 106850 (2019). [65] J. S. Moreland, J. E. Bernhard, and S. A. Bass, Alternative ansatz to wounded nucleon and binary collision scaling in highenergy nuclear collisions, Phys. Rev. C 92, 011901(R) (2015). [66] S. A. Bass et al., Microscopic models for ultrarelativistic heavy ion collisions, Prog. Part. Nucl. Phys. 41, 255 (1998). [67] M. Li, Y. Zhou, W. Zhao, B. Fu, Y. Mou, and H. Song, Investigations on mixed harmonic cumulants in heavy-ion collisions at energies available at the CERN Large Hadron Collider, Phys. Rev. C 104, 024903 (2021). [68] J. E. Bernhard, J. S. Moreland, S. A. Bass, J. Liu, and U. Heinz, Applying Bayesian parameter estimation to relativistic heavyion collisions: simultaneous characterization of the initial state and quark-gluon plasma medium, Phys. Rev. C 94, 024907 (2016). [69] E. G. Nielsen and Y. Zhou, Transverse momentum decorrelation of the flow vector in Pb-Pb collisions at √sNN =5.02 TeV, arXiv:2211.13651 [nucl-ex]. S. Acharya ,125,132 D. Adamová ,86 A. Adler,69 G. Aglieri Rinella ,32 M. Agnello ,29 N. Agrawal ,50 Z. Ahammed ,132 S. Ahmad ,15 S. U. Ahn ,70 I. Ahuja ,37 A. Akindinov ,140 M. Al-Turany ,98 D. Aleksandrov ,140 B. Alessandro ,55 H. M. Alfanda ,6R. Alfaro Molina ,66 B. Ali ,15 Y. Ali,13 A. Alici ,25 N. Alizadehvandchali ,114 A. Alkin ,32 J. Alme ,20 G. Alocco ,51 T. Alt ,63 I. Altsybeev ,140 M. N. Anaam ,6C. Andrei ,45 A. Andronic ,135 V. Anguelov ,95 F. Antinori ,53 P. Antonioli ,50 C. Anuj ,15 N. Apadula ,74 L. Aphecetche ,104 H. Appelshäuser ,63 C. Arata ,73 S. Arcelli ,25 M. Aresti ,51 R. Arnaldi ,55 I. C. Arsene ,19 M. Arslandok ,137 A. Augustinus ,32 R. Averbeck ,98 S. Aziz ,72 M. D. Azmi ,15 A. Badalà ,52 Y. W. Baek ,40 X. Bai ,118 R. Bailhache ,63 Y. Bailung ,47 R. Bala ,91 A. Balbino ,29 A. Baldisseri ,128 B. Balis ,2D. Banerjee ,4Z. Banoo ,91 R. Barbera ,26 L. Barioglio ,96 M. Barlou,78 G. G. Barnaföldi ,136 L. S. Barnby ,85 V. Barret ,125 L. Barreto ,110 C. Bartels ,117 K. Barth ,32 E. Bartsch ,63 F. Baruffaldi ,27 N. Bastid ,125 S. Basu ,75 G. Batigne ,104 D. Battistini ,96 B. Batyunya ,141 D. Bauri,46 J. L. Bazo Alba ,102 I. G. Bearden ,83 C. Beattie ,137 P. Becht ,98 D. Behera ,47 I. Belikov ,127 A. D. C. Bell Hechavarria ,135 F. Bellini ,25 R. Bellwied ,114 S. Belokurova ,140 V. Belyaev ,140 G. Bencedi ,136,64 S. Beole ,24 A. Bercuci ,45 Y. Berdnikov ,140 A. Berdnikova ,95 L. Bergmann ,95 M. G. Besoiu ,62 L. Betev ,32 P. P. Bhaduri ,132 A. Bhasin ,91 M. A. Bhat ,4B. Bhattacharjee ,41 L. Bianchi ,24 N. Bianchi ,48 J. Bielˇ cík ,35 J. Bielˇ cíková ,86 J. Biernat ,107 A. P. Bigot ,127 A. Bilandzic ,96 G. Biro ,136 S. Biswas ,4N. Bize ,104 J. T. Blair ,108 D. Blau ,140 M. B. Blidaru ,98 N. Bluhme,38 C. Blume ,63 G. Boca ,21,54 F. Bock ,87 T. Bodova ,20 A. Bogdanov,140 L051901-8