Linear and non-linear flow mode in Pb–Pb collisions at √sNN=2.76 TeV

Physics Letters B 773 (2017) 68–80 Contents lists available at ScienceDirect Physics Letters B www.elsevier.com/locate/physletb Linear and non-linear flow mode in Pb–Pb collisions at √sNN =2.76 TeV .ALICE Collaboration a r t i c l e i n f o a b s t r a c t Article history: Received 22 May 2017 Received in revised form 10 July 2017 Accepted 27 July 2017 Available online 4 August 2017 Editor: L. Rolandi The second and the third order anisotropic flow, V2and V3, are mostly determined by the corresponding initial spatial anisotropy coefficients, ε2and ε3, in the initial density distribution. In addition to their dependence on the same order initial anisotropy coefficient, higher order anisotropic flow, Vn(n >3), can also have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this Letter we investigate the linear and non-linear modes in higher order anisotropic flow Vnfor n =4, 5, 6 with the ALICE detector at the Large Hadron Collider. The measurements are done for particles in the pseudorapidity range |η| <0.8and the transverse momentum range 0.2 <pT<5.0GeV/cas a function of collision centrality. The results are compared with theoretical calculations and provide important constraints on the initial conditions, including initial spatial geometry and its fluctuations, as well as the ratio of the shear viscosity to entropy density of the produced system. ©2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. 1. Introduction The primary goal of the ultra-relativistic heavy-ion collision programme at the Large Hadron Collider (LHC) is to study the properties of the Quark–Gluon Plasma (QGP), anovel state of strongly interacting matter that is proposed to exist at high temperatures and energy densities [1,2]. Studies of azimuthal correlations of produced particles have contributed significantly to the characterisation of the matter created in heavy-ion collisions [3, 4]. Anisotropic flow, which quantifies the anisotropy of the momentum distribution of final state particles, is sensitive to the event-by-event fluctuating initial geometry of the overlap region, together with the transport properties and equation of state of the system [4–7]. The successful description of anisotropic flow results by hydrodynamic calculations suggests that the created medium behaves as a nearly perfect fluid [4,5] with a shear viscosity to entropy density ratio, η/s, close to a conjectured lower bound 1/4π[8]. Anisotropic flow is characterised using a Fourier decomposition of the particle azimuthal distribution in the plane transverse to the beam direction [9,10]: dN dϕ∝1+2∞  n=1 vncos[n(ϕ−n)],(1) where Nis the number of produced particles, ϕis the azimuthal angle of the particle and nis the nth order flow symmetry plane. E-mail address: [email protected]. The nth order (complex) anisotropic flow Vnis defined as: Vn≡ vneinn, where vn=|Vn|is the flow coefficient, and nrepresents the azimuth of Vnin momentum space. For non-central heavy-ion collisions, the dominant flow coefficient is v2, referred to as elliptic flow. Non-vanishing values of higher flow coefficients v3–v6at the LHC are ascribed primarily to the response of the produced QGP to fluctuations of the initial energy density profile of the colliding nucleons [11–15]. The standard (moment-defined) initial anisotropy coefficients εntogether with their corresponding initial symmetry planes (also called participant planes) ncan be calculated from the transverse positions (r, φ) of the participating nucleons εneinn≡−rneinφ rn(for n>1), (2) where  denotes the average over the transverse position of all participating nucleons, φis azimuthal angle, and nis the order of the coefficient [11,16]. It has been shown in [17,18] that V2 and V3are mostly determined with the same order initial spatial anisotropy coefficients ε2and ε3, respectively. Considering that η/sreduces the hydrodynamic response of vnto εn, it was proposed in [18–21] that vn/εn(for n =2, 3) could be a direct probe to quantitatively constrain the η/sof the QGP in hydrodynamic calculations. However, εncannot be determined experimentally. Instead, they are obtained from various theoretical models, resulting in large uncertainties in the estimated η/sderived indirectly from v2and v3measurements [17,19]. On the other hand, higher order anisotropic flow Vnwith n >3probe smaller spatial scales and http://dx.doi.org/10.1016/j.physletb.2017.07.060 0370-2693/©2017 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3. ALICE Collaboration / Physics Letters B 773 (2017) 68–80 69 thus are more sensitive to η/sthan V2and V3due to more pronounced viscous corrections [16,22]. Thus, the study of the full set of flow coefficients is expected to constrain both εnand η/ssimultaneously. However, it was realised later that Vnwith n >3is not linearly correlated with the corresponding εn[16,22,23], which makes the extraction of η/sfrom measurements of higher order flow coefficients less straightforward. In addition to the study of flow coefficients, the results of correlations between different order anisotropic flow angles and amplitudes shed light on both the early stage dynamics and the transport properties of the created QGP [24–32]. In particular, the characteristic pattern of flow symmetry plane correlations (also known as angular correlations of flow-vectors) observed in experiments is reproduced quantitatively by theoretical calculations [29–33]. However, the correlations between flow coefficients (also known as amplitude correlations of flow-vectors), investigated using symmetric cumulants, provide stricter constraints on initial conditions and η/sthan the individual vnmeasurements [24–28,31,32]. It is a challenge for current theoretical models to provide quantitative descriptions of the correlations between different order flow coefficients. As discussed above, it is known that the lower order anisotropic flow Vn(n =2, 3) is largely determined by a linear response of the system to the corresponding εn(except in peripheral collisions). Higher order anisotropic flow Vnwith n >3 have contributions not only from the linear response of the system to εn, but also contributions proportional to the product of ε2and/or ε3. These contributions are usually called non-linear response [25,34] in higher order anisotropic flow. For a single event, Vnwith n =4, 5 and 6 can be decomposed into the so-called linear and the non-linear contributions, according to V4=VNL 4+VL 4=χ4,22(V2)2+VL 4,(3) V5=VNL 5+VL 5=χ5,32V2V3+VL 5,(4) V6=VNL 6+VL 6 =χ6,222(V2)3+χ6,33(V3)2+χ6,42V2VL 4+VL 6.(5) Here χn,mk is a new observable called the non-linear mode coefficient [34] and VNL nrepresents the non-linear mode which has contributions from modes with lower order anisotropy coefficients. The VL nterm represents the linear mode, which was naïvely expected from the linear response of the system to the same order εn. However, a recent hydrodynamic calculation showed that VL nis not driven by the linear response to the standardly momentdefined εnintroduced in Eq. (2), but the corresponding cumulantdefined anisotropy coefficient ε n[30,35]. For example, VL 4is expected to be driven by the 4th-order cumulant-defined anisotropy coefficient and its corresponding initial symmetry plane which can be calculated as ε 4ei4 4≡−z4−3z22 r4=ε4ei44+3r22 r4ε2 2ei42,(6) where z=reiφ. The calculations for other order anisotropy coefficients and their corresponding initial symmetry planes can be found in [30,35]. If the non-linear and linear modes of higher order anisotropic flow, VNL nand VL n, are uncorrelated (e.g. VL nis perpendicular to VNL n), they can be isolated. One of the proposed approaches to validate the assumption that VNL nand VL nare uncorrelated is testing the following relations [25]: V4(V∗ 2)2v2 2 V4(V∗ 2)2v2 2=v6 2 v4 2v2 2,(7) V5V∗ 3V∗ 2v2 2 V5V∗ 3V∗ 2v2 2=v4 2v2 3 v2 2v2 3v2 2.(8) If the above relations are valid, one could combine the analyses of higher order anisotropic flow with respect to their corresponding symmetry planes and to the planes of lower order anisotropic flow V2or V3to eliminate the uncertainty from initial state assumptions and extract η/swith better precision [34]. In this Letter, the linear and non-linear modes in higher order anisotropic flow generation are studied in Pb–Pb collisions at √sNN =2.76 TeV with the ALICE detector. The main observables are introduced in Section 2and the experimental setup is described in Section 3. Section 4presents the study of the systematic uncertainties of the above mentioned observables. The results and their discussion are provided in Section 5. Section 6contains the summary and conclusions. 2. Observables and analysis methods Ideally, the flow coefficient vncan be measured via the azimuthal correlations of emitted particles with respect to the symmetry plane nas vn=cosn(ϕ−n). Since nis unknown experimentally, the simplest approach to obtain vnis using 2-particle correlations: vn{2}=cosn(ϕ1−ϕ2)1/2=v2 n1/2 .(9) Here   denotes the average over all particles in a single event and then an average of over all events,  indicates the event average of over all events, and ϕirepresents the azimuthal angle of the i-th particle. The analysed events are divided into two sub-events A and B, separated by a pseudorapidity gap, to suppress non-flow effects. The latter are the azimuthal correlations not associated to the common symmetry plane n, such as jets and resonance decays. Thus, we modify Eq. (9) to vn{2}=cos(nϕA 1−nϕB 2)1/2=v2 n1/2 .(10) Here ϕA 1and ϕB 2are selected from subevent A and B, respectively. Before introducing observables related to the linear and nonlinear modes in higher order anisotropic flow, it is crucial to verify whether Eqs. (7)–(8) are applicable. The left and right hand sides of Eq. (7) are obtained by constructing suitable multi-particle correlations [34]: V4(V∗ 2)2v2 2A V4(V∗ 2)2Av2 2 =cos(4ϕA 1+2ϕA 2−2ϕB 3−2ϕB 4−2ϕB 5) cos(4ϕA 1−2ϕB 2−2ϕB 3)cos(2ϕA 1−2ϕB 2),(11) v6 2 v4 2v2 2 =cos(2ϕA 1+2ϕA 2+2ϕA 3−2ϕB 4−2ϕB 5−2ϕB 6) cos(2ϕA 1+2ϕA 2−2ϕB 3−2ϕB 4)cos(2ϕA 1−2ϕB 2).(12) Similarly, we can validate Eq. (8) by calculating both sides with [34]: V5V∗ 3V∗ 2v2 2A V5V∗ 3V∗ 2Av2 2 =cos(5ϕA 1+2ϕA 2−3ϕB 3−2ϕB 4−2ϕB 5) cos(5ϕA 1−3ϕB 2−2ϕB 3)cos(2ϕA 1−2ϕB 2),(13) 70 ALICE Collaboration / Physics Letters B 773 (2017) 68–80 v4 2v2 3 v2 2v2 3v2 2 =cos(3ϕA 1+2ϕA 2+2ϕA 3−3ϕB 4−2ϕB 5−2ϕB 6) cos(3ϕA 1+2ϕA 2−3ϕB 3−2ϕB 4)cos(2ϕA 1−2ϕB 2).(14) The magnitude of VNL nwas denoted as vn{m}(here mis the lower order flow symmetry plane and m =2, 3) in [34]. The notation vn,mk, where nspecifies the order of the flow term while mand ketc. denote the contributing lower order flow symmetry planes, is used in this Letter. If the linear and non-linear modes are independent, then the non-linear mode in higher order anisotropic flow can be analysed by correlating Vnwith 2or/and 3[34]. For sub-event A we can define: vA 4,22 =cos(4ϕA 1−2ϕB 2−2ϕB 3) cos(2ϕA 1+2ϕA 2−2ϕB 3−2ϕB 4) ,(15) vA 5,32 =cos(5ϕA 1−3ϕB 2−2ϕB 3) cos(3ϕA 1+2ϕA 2−3ϕB 3−2ϕB 4) ,(16) vA 6,222 =cos(6ϕA 1−2ϕB 2−2ϕB 3−2ϕB 4) cos(2ϕA 1+2ϕA 2+2ϕA 3−2ϕB 4−2ϕB 5−2ϕB 6) ,(17) vA 6,33 =cos(6ϕA 1−3ϕB 2−3ϕB 3) cos(3ϕA 1+3ϕA 2−3ϕB 3−3ϕB 4) .(18) Similarly, one can obtain vB n,mk for sub-event B. The average of vA n,mk and vB n,mk, defined as vn,mk, quantifies the magnitude of the non-linear mode in higher order anisotropic flow, which can be written as [36]: v4,22 =v4v2 2cos(44−42) v4 2≈v4cos(44−42),(19) v5,32 =v5v3v2cos(55−33−22) v2 3v2 2 ≈v5cos(55−33−22),(20) v6,222 =v6v3 2cos(66−62) v6 2≈v6cos(66−62),(21) v6,33 =v6v2 3cos(66−63) v4 3≈v6cos(66−63).(22) The approximation is valid if the correlation between lower (n = 2, 3) and higher (n >3) flow coefficients is weak. As can be seen in Eqs. (3)–(5), the calculation for V6is more complicated than V4and V5, and the exact expression for vL 6is currently not available. Therefore, we only focus on the two nonlinear modes of V6without discussing vL 6. According to Eqs. (3) to (4), the magnitudes of the linear mode in higher order anisotropic flow can be calculated as: vL 4=v2 4{2}−v2 4,22,(23) vL 5=v2 5{2}−v2 5,32.(24) The ratio of vn,mk to vn{2}, denoted as ρn,mk, can be calculated as: ρ4,22 =v4,22 v4{2}=cos(44−42),(25) ρ5,32 =v5,32 v5{2}=cos(55−33−22),(26) ρ6,222 =v6,222 v6{2}=cos(66−62),(27) ρ6,33 =v6,33 v6{2}=cos(66−63).(28) These observables measure the correlations between different order flow symmetry planes if the correlations between different order flow coefficients are weak. They are very similar to the socalled weighted event-plane correlations measured by the ATLAS Collaboration [33]. The differences are as follows: v2 2v2 3is used in Eq. (20) and (26), while v2 2v2 3was used in [33], which did not consider the anti-correlations between v2and v3found in [27]. In addition, multi-particle correlations are used for v2and v3in the denominator of the observables, while two-particle correlations are used in the event-plane correlations which might be biased from fluctuations of v2and v3. The non-linear mode coefficients χn,mk in Eqs. (3) to (5) are defined as: χ4,22 =v4,22 v4 2 (29) χ5,32 =v5,32 v2 2v2 3 (30) χ6,222 =v6,222 v6 2 (31) χ6,33 =v6,33 v4 3 .(32) These quantify the contributions of the non-linear mode and are expected to be independent of v2or v3. All of the observables above are based on 2- and multi-particle correlations, which can be obtained using the generic framework for anisotropic flow analyses introduced in Ref. [24]. 3. Experimental setup and data analysis The data samples analysed in this Letter were recorded by ALICE during the Pb–Pb runs of the LHC at a centre-of-mass energy of √sNN =2.76 TeV in 2010. Minimum bias Pb–Pb collision events were triggered by the coincidence of signals in the V0 detector [37,38], with an efficiency of 98.4% of the hadronic cross section [39]. The V0 detector is composed of two arrays of scintillator counters, V0-A and V0-C, which cover the pseudorapidity ranges 2.8 <η<5.1 and −3.7 <η<−1.7, respectively. Beam background events were rejected using the timing information from the V0 and the Zero Degree Calorimeter (ZDC) [37] detectors and by correlating reconstructed clusters and tracklets with the Silicon Pixel Detectors (SPD). The fraction of pile-up events in the data sample is found to be negligible after applying dedicated pileup removal criteria [40]. Only events with a reconstructed primary vertex within ±10 cm from the nominal interaction point along the beam direction were used in this analysis. The primary vertex was estimated using tracks reconstructed by the Inner Tracking System (ITS) [37,41] and Time Projection Chamber (TPC) [37,42]. The collision centrality was determined from the measured V0 amplitude and centrality intervals were defined following the procedure described in [39]. About 13 million Pb–Pb events passed all of the event selection criteria. ALICE Collaboration / Physics Letters B 773 (2017) 68–80 71 Tracks reconstructed using the combined information from the TPC and ITS are used in this analysis. This combination ensures a high detection efficiency, optimum momentum resolution, and a minimum contribution from photon conversions and secondary charged particles produced either in the detector material or from weak decays. To reduce the contributions from secondaries, charged tracks were required to have a distance of closest approach to the primary vertex in the longitudinal (z) direction and transverse (xy) plane smaller than 3.2 cm and 2.4 cm, respectively. Additionally, tracks were required to have at least 70 TPC space points out of the maximum 159. The average χ2per degree of freedom of the track fit to the TPC space points was required to be below 2. In this study, tracks were selected in the pseudorapidity range |η| <0.8 and the transverse momentum range 0.2 <pT<5.0GeV/c. 4. Systematic uncertainties Numerous sources of systematic uncertainty were investigated by varying the event and track selection as well as the uncertainty associated with the possible remaining non-flow effects in the analysis. The variation of the results with the collision centrality is calculated by alternatively using the TPC or SPD to estimate the event multiplicity and is found to be less than 3% for all observables. Results with opposite polarities of the magnetic field within the ALICE detector and with narrowing the nominal ±10 cm range of the reconstructed vertex along the beam direction from the centre of the ALICE detector to 9, 8 and 7 cm do not show a difference of more than 2% compared to the default selection criteria for various measurements. The contributions from pile-up events to the final systematic uncertainty are found to be negligible. The sensitivity to the track selection criteria was explored by varying the number of TPC space points and by using tracks reconstructed in the TPC alone. Varying the number of TPC space points from 70 to 80, 90 and 100 out of a possible 158, results in a 1–3% variation of the results for vn, within 1.5% for ρn,mk and χn,mk. Using TPC-only tracks leads to a difference of less than 14%, 17% and 8% for vn, ρn,mk and χn,mk, respectively. Both effects were included in the evaluation of the systematic uncertainty. Several different approaches have been applied to estimate the effects of non-flow. These include the investigation of multi-particle correlations with various |η|gaps, the application of the like-sign technique which correlates two particles with either all positive or negative charges and suppress such non-flow as due to resonance decays, as well as the calculations using HIJING Monte Carlo simulations [43], which do not include anisotropic flow. It was found that the possible remaining non-flow effects are less than 10.5%, 11% and 7% for vn, ρn,mk and χn,mk, respectively. They are taken into account in the final systematic uncertainty. The systematic uncertainties evaluated for each source mentioned above were added in quadrature to obtain the total systematic uncertainty of the measurements. 5. Results and discussion As discussed in Sec. 2, one can validate the assumption that linear and non-linear modes in higher order anisotropic flow are uncorrelated via Eqs. (7) and (8). These have been tested in A Multi-Phase Transport (AMPT) model [25] as well as in the hydrodynamic calculations [44]. Good agreement between left- and right-hand sides of Eqs. (7) and (8) is found for all centrality classes, independent of the initial conditions and the ideal or viscous fluid dynamics used in the calculations. Thus, it is crucial to check these equalities in data, to further confirm the assumption that the two components are uncorrelated and can be isolated independently. Fig. 1 confirms that the agreement observed Fig. 1. Study of relationship between linear and non-linear modes in higher order anisotropic flow in Pb–Pb collisions at √sNN =2.76 TeV, according to Eqs. (7) and (8). in theoretical calculations is also present in the data despite small deviations found in central collisions when testing Eqs. (8). Their centrality dependency are similar as the previous theoretical predictions [25,44]. The measurements support the assumption that higher order anisotropic flow Vn(n >3) can be modeled as the sum of independent linear and non-linear modes. The magnitudes of linear and non-linear modes in higher order anisotropic flow are reported as a function of collision centrality in Fig. 2. In this Letter, sub-events A and B are built in the pseudorapidity ranges −0.8 <η<−0.4 and 0.4 <η<0.8, respectively, which results in a pseudorapidity gap of |η| >0.8for all presented measurements. It can be seen that the linear mode vL 4depends weakly on centrality and is the larger contribution to v4{2}for the centrality range 0–30%. The non-linear mode, v4,22, increases monotonically as the centrality decreases and saturates around centrality percentile 50%, becoming the dominant source for centrality intervals above 40%. Similar trends of centrality dependence have been observed for V5, although v5,32 becomes the dominant contribution in centrality percentile above 30%. Only two non-linear components v6,222 and v6,33 are discussed for V6. It is shown in Fig. 2 (right) that v6,222 increases monotonically as the centrality decreases to centrality 50%, while v6,33 has a weaker centrality dependence compared to v6,222. The linear and non-linear modes in higher order anisotropic flow were investigated by the ATLAS Collaboration [26] using a different approach based on “Event Shape Engineering” [45]. With this method one can utilise large fluctuations in the initial geometry of the system to select events corresponding to a specific initial shape. The conclusion is qualitatively consistent with what is reported here, although a direct comparison is not possible due to the different kinematic cuts (especially the integrated pTrange) used in the two measurements. The higher order anisotropic flow induced by lower order anisotropic flow were also measured using the event-plane method at the LHC [14,46]. However, the measurements of the non-linear mode presented in this Letter are based on the multi-particle correlations method with a |η| gap. This method makes it easier to measure an observable like v5,32, which is less straightforward to define using the event plane method [14,46]. In addition, as pointed out in [25,34,47], this new multi-particle correlations method should strongly suppress short-range (in pseudorapidity) non-flow effects and provides a robust measurement without any dependence on the experimental acceptance. The measurements are compared to recent hydrodynamic calculations from a hybrid IP-Glasma +MUSIC +UrQMD model [48], in which realistic event-by-event initial conditions are used and the hydrodynamic evolution takes into account both shear and bulk viscosity. It is shown that this hydrodynamic calculation could describe quantitatively the total magnitudes of V4 and V6, as well as the magnitudes of their linear and non-linear modes, while it slightly overestimates the results for V5. The centrality dependence of ρn,mk, which quantifies the angular correlations between different order flow symmetry planes, is 72 ALICE Collaboration / Physics Letters B 773 (2017) 68–80 Fig. 2. Centrality dependence of v4(left), v5(middle) and v6(right) in Pb–Pb collisions at √sNN =2.76 TeV. Contributions from linear and non-linear modes are presented with open and solid markers, respectively. The hydrodynamic calculations from IP-Glasma +MUSIC +UrQMD [48] are shown for comparison. Fig. 3. Centrality dependence of ρn,mk in Pb–Pb collisions at √sNN =2.76 TeV. ATLAS measurements based on the event-plane correlation [33] are presented with open markers. The hydrodynamic calculations from IP-Glasma +MUSIC +UrQMD [48] are shown with open bands. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) presented in Fig. 3. It is observed that ρ4,22 increases from central to peripheral collisions, which suggests that the correlations between 2and 4are stronger in peripheral than in central collisions. It implies that VNL 4tends to align with V4in more peripheral collisions. The results of ρ6,33, which measures the correlation of 3and 6, do not exhibit a strong centrality dependence within the statistical uncertainties. As mentioned above, ρ4,22 and ρ6,33 are similar to the previous “event-plane correlation” measurements cos(44−42)wand cos(66−63)w in [33]. The comparisons between measurements of these observables are also presented in Fig. 3. The results are compatible with each other, despite the different kinematic ranges used by ATLAS and this analysis. It should be also noted that the measurements of ρn,mk presented in this Letter show the symmetry plane correlations at mid-pseudorapidity |η| <0.8 while ATLAS measured the symmetry plane correlations using −4.8 <η<−0.5 and 0.5 <η<4.8for two-plane correlations, and using −2.7 < η<−0.5, 0.5 <η<2.7 and 3.3 <|η| <4.8for 3-plane correlations [33]. Previous investigations suggest that there might be η-dependent fluctuations of the flow symmetry plane and the flow magnitude [49,50]. As a consequence, one might expect a difference when measuring the correlations of flow symmetry planes from different pseudorapidity regions. However, Fig. 3 shows good agreement between the ALICE and ATLAS measurements. Therefore, no obvious indication that the flow symmetry plane varies with ηcan be deduced from this comparison. It is noticeable in Fig. 3 that the ρ5,32 measurement seems slightly higher than the cos(55−33−22)wmeasurement. This is mainly due to a small difference between the definitions of the observable as introduced in Sec. 2: the term v2 2v2 31/2is used in ρ5,32, whereas v2 21/2v2 31/2is used in the “event-plane correlations” [33]. Considering the known anti-correlations between v2and v3[26,27], v2 2v2 31/2could be up to 10% lower than v2 21/2v2 31/2depending on the centrality class [27], leading to a slightly larger ρ5,32 than cos(55−33−22)wfrom ATLAS. It has been observed in hydrodynamic and transport model calculations that the symmetry plane correlations, e.g. correlations of second and fourth order symmetry planes, change sign during the system evolution [29,30,32]. The measured flow symmetry plane correlations could be nicely explained by the combination of contributions from linear and non-linear modes in higher order anisotropic flow [30]. This indicates that the flow symmetry plane correlation ρn,mk carries important information about the dynamic evolution of the created system. In addition, the model calculations suggest that stronger initial symmetry plane correlations are reflected in stronger correlations between the flow symmetry planes in the final state [29,32]. And a larger value of η/sof the QGP leads to weaker flow symmetry plane correlations in the final state. As pointed out in [29], the hydrodynamic calculations from VISH2 +1using Monte Carlo Glauber (MC-Glb) or Monte Carlo Kharzeev–Levin–Nardi (MC-KLN) initial conditions can only describe qualitatively the trends of the centrality dependence of the event-plane correlation measurements by ATLAS. It is therefore expected that these hydrodynamic calculations cannot describe the presented ALICE measurements, which are compatible with the ATLAS event-plane correlation measurements. Fig. 3 shows that the hydrodynamic calculations from IP-Glasma +MUSIC +UrQMD [48] reproduce nicely the measurements of symmetry plane correlations ρn,mk. The measurements of ρn,mk presented in this Letter, together with the comparison to hydrodynamic calculations, should place constraints on the initial conditions and η/sof the QGP in hydrodynamic calculations. Fig. 4 presents the measurements of the non-linear mode coefficients as a function of collision centrality. It is observed that χ4,22 and χ6,222 decrease modestly from central to mid-central collisions, and stay almost constant from mid-central to more peripheral collisions. For χ5,32 and χ6,33 strong centrality dependence is not observed either. Thus, the dramatic increase of vn,mk shown in Fig. 2 appears to be mainly due to the increase of v2and/or v3from central to peripheral collisions and not the increase of the non-linear mode coefficient. It is also noteworthy that the relationship of χ4,22 ∼χ6,33 ≈χ5,32 2is approximately valid, as predicted by hydrodynamic calculations [34]. The comparisons to event-by- event viscous hydrodynamic calculations from VISH2 +1[44] and from IP-Glasma +MUSIC +UrQMD [48] are also presented in Fig. 4. VISH2 +1shows that χ4,22 calculations with MC-Glb initial conditions are larger than those with MC-KLN initial conditions, i.e. χ4,22 depends on the initial conditions. At the same time, ALICE Collaboration / Physics Letters B 773 (2017) 68–80 73 Fig. 4. Centrality dependence of χin Pb–Pb collisions at √sNN =2.76 TeV. Hydrodynamic calculations from VISH2 +1[44] are shown in shaded areas and the one from IP-Glasma +MUSIC +UrQMD [48] are shown with open bands. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.) the curves with different η/svalues for VISH2 +1are very similar, indicating that χ4,22 is insensitive to η/s. The measurements favour IP-Glasma and MC-KLN over MC-Glb initial conditions regardless of η/s. This suggests that the χ4,22 measurement can be used to constrain the initial conditions, with less concern of the setting of η/s(T)in hydrodynamic calculations than previous flow observables. It was predicted that χ6,222 <χ6,33 based on the ideal hydrodynamic calculation using smooth initial Gaussian density profiles [34], whereas an opposite prediction was obtained in the ideal hydrodynamic calculation evolving genuinely bumpy initial conditions obtained from a Monte Carlo sampling of the initial nucleon positions in the colliding nuclei [44]. It is seen in Fig. 4 that χ6,222 ∼χ6,33 within the current uncertainties. The data are not able to discriminate the different predictions in [34] and [44]. Hydrodynamic calculations using MC-KLN and IP-Glasma initial conditions give better descriptions of χ6,222, compared to the ones using MC-Glb initial conditions. For χ5,32 none of the combinations of initial conditions and η/sin the hydrodynamic calculations agree quantitatively with data. This might be due to the current difficulty of describing the anti-correlations between v2and v3 in hydrodynamic calculations [27,51], which are involved in the calculation of χ5,32. Furthermore, VISH2 +1calculations show that χ5,32 and χ6,33 are very weakly sensitive to the initial conditions, but decrease as η/sincreases. The investigation with the VISH2 +1hydrodynamic framework shows that the sensitivity of χ5,32 and χ6,33 to η/sis not due to sensitivity to shear viscous effects during the buildup of hydrodynamic flow. Instead, as found in [44], it is due to the η/sat freeze-out. The measurements of χ5,32 and χ6,33 do not further constrain the η/sduring system evolution, however, they provide unique information on η/sat freeze-out which was poorly known and cannot be obtained from other anisotropic flow related observables. Further improvement of model calculations on correlations between different order flow coefficients are necessary to better understand the comparison of χ5,32 obtained from data and hydrodynamic calculations. The χ6,33 results are consistent with hydrodynamic calculations from VISH2 +1with MC-KLN initial conditions using η/s =0.08 and IP-Glasma +MUSIC +UrQMD with a η/s =0.095. It is shown that χ5,32 and χ6,33 have a weak centrality dependence if a smaller η/sis used in the hydrodynamic calculations. Such a weak centrality dependence of χ5,32 and χ6,33 is observed in data as well. The measurements presented here suggest a small η/svalue at freeze-out, which can be useful to constrain the temperature dependence of the shear viscosity over entropy density ratio, η/s(T), in the development of hydrodynamic frameworks. These results suggest that future tuning of the parameterisations of η/s(T)in hydrodynamic frameworks using the presented measurements is necessary. 6. Summary The linear and non-linear modes in higher order anisotropic flow generation were studied with 2- and multi-particle correlations in Pb–Pb collisions at √sNN =2.76 TeV. The results presented in this Letter show that higher order anisotropic flow can be isolated into two independent contributions: the component that arises from a non-linear response of the system to the lower order initial anisotropy coefficients ε2and/or ε3, and a linear mode which is driven by linear response of the system to the same order cumulant-defined anisotropy coefficient. Aweak centrality dependence is observed for the contributions from linear mode whereas the contributions from non-linear mode increase dramatically as the collision centrality decreases, and it becomes the dominant source in higher order anisotropic flow in mid-central to peripheral collisions. It is shown that this is mainly due to the increase of lower order flow coefficients v2and v3. The correlations between different flow symmetry planes are measured. The results are compatible with the previous “event-plane correlation” measurements, and can be quantitatively described by calculations using the IP-Glasma +MUSIC +UrQMD framework. Furthermore, non-linear mode coefficients, which have different sensitivities to the shear viscosity over entropy density ratio η/sand the initial conditions, are presented in this Letter. Comparisons to hydrodynamic calculations suggest that the data is described better by hydrodynamic calculations with smaller η/s. In addition, the MC- Glb initial condition is disfavoured by the presented results. Measurements of linear and non-linear modes in higher order anisotropic flow and their comparison to hydrodynamic calculations provide more precise constraints on the initial conditions and temperature dependence of η/s. These results could also offer new insights into the geometry of the fluctuating initial state and into the dynamical evolution of the strongly interacting medium produced in relativistic heavy-ion collisions at the LHC. Acknowledgements 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 and Österreichische 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), Universidade Federal do Rio Grande do Sul (UFRGS), Financiadora de Estudos e Projetos (Finep) and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), 74 ALICE Collaboration / Physics Letters B 773 (2017) 68–80 Brazil; Ministry of Science & Technology of China (MSTC), National Natural Science Foundation of China (NSFC) and Ministry of Education of China (MOEC), China; Ministry of Science, Education and Sports and Croatian Science Foundation, Croatia; Ministry of Education, Youth and Sports of the Czech Republic, Czech Republic; The Danish Council for Independent Research — Natural Sciences, the Carlsberg Foundation 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, Wissenschaft, Forschung und Technologie (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) and Council of Scientific and Industrial Research (CSIR), New Delhi, India; Indonesian Institute of Science, Indonesia; Centro Fermi -Museo Storico della Fisica e Centro Studi e Ricerche Enrico Fermi and Istituto Nazionale di Fisica Nucleare (INFN), Italy; Institute for Innovative Science and Technology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHI and Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan; Consejo Nacional de Ciencia y Tecnología (CONACYT), through Fondo de Cooperatión Internacional en Ciencia y Tecnología (FONCICYT) and Dirección General de Asuntos del Personal Académico (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 Science and Higher Education and National Science Centre, 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 and Romanian National Agency for Science, Technology and Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministry of Education and Science of the Russian Federation and National Research Centre Kurchatov Institute, Russia; Ministry of Education, Science, Research and Sport of the Slovak Republic, Slovakia; National Research Foundation of South Africa, South Africa; Centro de Aplicaciones Tecnológicas y Desarrollo Nuclear (CEADEN), Cubaenergía, Cuba; Ministerio de Ciencia e Innovación and Centro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT), Spain; Swedish Research Council (VR) and Knut & Alice Wallenberg Foundation (KAW), Sweden; European Organization for Nuclear Research, Switzerland; National Science and Technology Development Agency (NSDTA), Suranaree University of Technology (SUT) and Office of the Higher Education Commission under NRU project of Thailand, Thailand; Turkish Atomic Energy Agency (TAEK), 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. References [1] E.V. Shuryak, Quark–gluon plasma and hadronic production of leptons, photons and pions, Phys. Lett. B 78 (1978) 150, Yad. Fiz. 28 (1978) 796. [2] E.V. Shuryak, Quantum chromodynamics and the theory of superdense matter, Phys. Rep. 61 (1980) 71–158. [3] J.-Y. Ollitrault, Anisotropy as a signature of transverse collective flow, Phys. Rev. D 46 (1992) 229–245. [4] S.A. Voloshin, A.M. Poskanzer, R. Snellings, Collective phenomena in noncentral nuclear collisions, arXiv:0809.2949 [nucl-ex]. [5] U. Heinz, R. Snellings, Collective flow and viscosity in relativistic heavy-ion collisions, Annu. Rev. Nucl. Part. Sci. 63 (2013) 123–151, arXiv:1301.2826 [nucl-th]. [6] S. Pratt, E. Sangaline, P. Sorensen, H. Wang, Constraining the equation of state of super-hadronic matter from heavy-ion collisions, Phys. Rev. Lett. 114 (2015) 202301, arXiv:1501.04042 [nucl-th]. [7] H. Song, Y. Zhou, K. Gajdosova, Collective flow and hydrodynamics in large and small systems at the LHC, Nucl. Sci. Tech. 28 (7) (2017) 99, arXiv:1703.00670 [nucl-th]. [8] P. Kovtun, D.T. Son, A.O. Starinets, Viscosity in strongly interacting quantum field theories from black hole physics, Phys. Rev. Lett. 94 (2005) 111601, arXiv:hep-th/0405231. [9] S. Voloshin, Y. Zhang, Flow study in relativistic nuclear collisions by Fourier expansion of Azimuthal particle distributions, Z. Phys. C 70 (1996) 665–672, arXiv:hep-ph/9407282. [10] A.M. Poskanzer, S.A. Voloshin, Methods for analyzing anisotropic flow in relativistic nuclear collisions, Phys. Rev. C 58 (1998) 1671–1678, arXiv:nuclex/9805001. [11] B. Alver, G. Roland, Collision geometry fluctuations and triangular flow in heavy-ion collisions, Phys. Rev. C 81 (2010) 054905, arXiv:1003.0194 [nucl-th], Phys. Rev. C 82 (2010) 039903 (Erratum). [12] ALICE Collaboration, K. Aamodt, et al., Higher harmonic anisotropic flow measurements of charged particles in Pb–Pb collisions at √sNN =2.76 TeV, Phys. Rev. Lett. 107 (2011) 032301, arXiv:1105.3865 [nucl-ex]. [13] ATLAS Collaboration, G. Aad, et al., 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 (2012) 014907, arXiv:1203.3087 [hep-ex]. [14] CMS Collaboration, S. Chatrchyan, et al., Measurement of higher-order harmonic azimuthal anisotropy in PbPb collisions at √sNN =2.76 TeV, Phys. Rev. C 89 (4) (2014) 044906, arXiv:1310.8651 [nucl-ex]. [15] ALICE Collaboration, J. Adam, et al., Anisotropic flow of charged particles in Pb–Pb collisions at √sNN =5.02 TeV, Phys. Rev. Lett. 116 (13) (2016) 132302, arXiv:1602.01119 [nucl-ex]. [16] B.H. Alver, C. Gombeaud, M. Luzum, J.-Y. Ollitrault, Triangular flow in hydrodynamics and transport theory, Phys. Rev. C 82 (2010) 034913, arXiv:1007.5469 [nucl-th]. [17] Z. Qiu, C. Shen, U. Heinz, Hydrodynamic elliptic and triangular flow in Pb–Pb collisions at √s=2.76 A TeV, Phys. Lett. B 707 (2012) 151–155, arXiv:1110.3033 [nucl-th]. [18] H. Niemi, G.S. Denicol, H. Holopainen, P. Huovinen, Event-by-event distributions of azimuthal asymmetries in ultrarelativistic heavy-ion collisions, Phys. Rev. C 87 (5) (2013) 054901, arXiv:1212.1008 [nucl-th]. [19] H. Song, S.A. Bass, U. Heinz, T. Hirano, C. Shen, 200 A GeV Au +Au collisions serve a nearly perfect quark–gluon liquid, Phys. Rev. Lett. 106 (2011) 192301, arXiv:1011.2783, Phys. Rev. Lett. 109 (2012) 139904 (Erratum). [20] F.G. Gardim, J. Noronha-Hostler, M. Luzum, F. Grassi, Effects of viscosity on the mapping of initial to final state in heavy ion collisions, Phys. Rev. C 91 (3) (2015) 034902, arXiv:1411.2574 [nucl-th]. [21] J. Fu, Centrality dependence of mapping the hydrodynamic response to the initial geometry in heavy-ion collisions, Phys. Rev. C 92 (2) (2015) 024904. [22] D. Teaney, L. Yan, Non linearities in the harmonic spectrum of heavy ion collisions with ideal and viscous hydrodynamics, Phys. Rev. C 86 (2012) 044908, arXiv:1206.1905 [nucl-th]. [23] F.G. Gardim, F. Grassi, M. Luzum, J.-Y. Ollitrault, Mapping the hydrodynamic response to the initial geometry in heavy-ion collisions, Phys. Rev. C 85 (2012) 024908, arXiv:1111.6538 [nucl-th]. [24] A. Bilandzic, C.H. Christensen, K. Gulbrandsen, A. Hansen, Y. Zhou, Generic framework for anisotropic flow analyses with multiparticle azimuthal correlations, Phys. Rev. C 89 (6) (2014) 064904, arXiv:1312.3572 [nucl-ex]. [25] R.S. Bhalerao, J.-Y. Ollitrault, S. Pal, Characterizing flow fluctuations with moments, Phys. Lett. B 742 (2015) 94–98, arXiv:1411.5160 [nucl-th]. [26] ATLAS Collaboration, G. Aad, et al., Measurement of the correlation between flow harmonics of different order in lead–lead collisions at √sNN =2.76 TeV with the ATLAS detector, Phys. Rev. C 92 (3) (2015) 034903, arXiv:1504.01289 [hep-ex]. [27] ALICE Collaboration, J. Adam, et al., Correlated event-by-event fluctuations of flow harmonics in Pb–Pb collisions at √sNN =2.76 TeV, Phys. Rev. Lett. 117 (2016) 182301, arXiv:1604.07663 [nucl-ex]. [28] Y. Zhou, Review of anisotropic flow correlations in ultrarelativistic heavy-ion collisions, Adv. High Energy Phys. 2016 (2016) 9365637, arXiv:1607.05613 [nucl-ex]. [29] Z. Qiu, U. Heinz, Hydrodynamic event-plane correlations in Pb +Pb collisions at √s=2.76 A TeV, Phys. Lett. B 717 (2012) 261–265, arXiv:1208.1200 [nuclth]. [30] D. Teaney, L. Yan, Event-plane correlations and hydrodynamic simulations of heavy ion collisions, Phys. Rev. C 90 (2) (2014) 024902, arXiv:1312.3689 [nuclth]. ALICE Collaboration / Physics Letters B 773 (2017) 68–80 75 [31] H. Niemi, K.J. Eskola, R. Paatelainen, Event-by-event fluctuations in a perturbative QCD +saturation +hydrodynamics model: determining QCD matter shear viscosity in ultrarelativistic heavy-ion collisions, Phys. Rev. C 93 (2) (2016) 024907, arXiv:1505.02677 [hep-ph]. [32] Y. Zhou, K. Xiao, Z. Feng, F. Liu, R. Snellings, Anisotropic distributions in a multiphase transport model, Phys. Rev. C 93 (3) (2016) 034909, arXiv:1508.03306 [nucl-ex]. [33] ATLAS Collaboration, G. Aad, et al., Measurement of event-plane correlations in √sNN =2.76 TeV lead–lead collisions with the ATLAS detector, Phys. Rev. C 90 (2) (2014) 024905, arXiv:1403.0489 [hep-ex]. [34] L. Yan, J.-Y. Ollitrault, ν4, ν5, ν6, ν7: nonlinear hydrodynamic response versus LHC data, Phys. Lett. B 744 (2015) 82–87, arXiv:1502.02502 [nucl-th]. [35] J. Qian, U. Heinz, R. He, L. Huo, Differential flow correlations in relativistic heavy-ion collisions, Phys. Rev. C 95 (5) (2017) 054908, arXiv:1703.04077 [nucl-th]. [36] R.S. Bhalerao, J.-Y. Ollitrault, S. Pal, Event-plane correlators, Phys. Rev. C 88 (2013) 024909, arXiv:1307.0980 [nucl-th]. [37] ALICE Collaboration, K. Aamodt, et al., The ALICE experiment at the CERN LHC, J. Instrum. 3 (2008) S08002. [38] ALICE Collaboration, E. Abbas, et al., Performance of the ALICE VZERO system, J. Instrum. 8 (2013) P10016, arXiv:1306.3130 [nucl-ex]. [39] ALICE Collaboration, B. Abelev, et al., Centrality determination of Pb–Pb collisions at √sNN =2.76 TeV with ALICE, Phys. Rev. C 88 (4) (2013) 044909, arXiv:1301.4361 [nucl-ex]. [40] ALICE Collaboration, B.B. Abelev, et al., Performance of the ALICE experiment at the CERN LHC, Int. J. Mod. Phys. A 29 (2014) 1430044, arXiv:1402.4476 [nuclex]. [41] ALICE Collaboration, K. Aamodt, et al., Alignment of the ALICE inner tracking system with cosmic-ray tracks, J. Instrum. 5 (2010) P03003, arXiv:1001.0502 [physics.ins-det]. [42] J. Alme, et al., The ALICE TPC, alarge 3-dimensional tracking device with fast readout for ultra-high multiplicity events, Nucl. Instrum. Methods Phys. Res., Sect. A, Accel. Spectrom. Detect. Assoc. Equip. 622 (2010) 316–367, arXiv:1001.1950 [physics.ins-det]. [43] M. Gyulassy, X.-N. Wang, HIJING 1.0: aMonte Carlo program for parton and particle production in high-energy hadronic and nuclear collisions, Comput. Phys. Commun. 83 (1994) 307, arXiv:nucl-th/9502021. [44] J. Qian, U.W. Heinz, J. Liu, Mode-coupling effects in anisotropic flow in heavyion collisions, Phys. Rev. C 93 (6) (2016) 064901, arXiv:1602.02813 [nucl-th]. [45] J. Schukraft, A. Timmins, S.A. Voloshin, Ultra-relativistic nuclear collisions: event shape engineering, Phys. Lett. B 719 (2013) 394–398, arXiv:1208.4563 [nucl-ex]. [46] ALICE Collaboration, B. Abelev, et al., Anisotropic flow of charged hadrons, pions and (anti-)protons measured at high transverse momentum in Pb–Pb collisions at √sNN =2.76 TeV, Phys. Lett. B 719 (2013) 18–28, arXiv:1205.5761 [nucl-ex]. [47] M. Luzum, J.-Y. Ollitrault, Eliminating experimental bias in anisotropic-flow measurements of high-energy nuclear collisions, Phys. Rev. C 87 (4) (2013) 044907, arXiv:1209.2323 [nucl-ex]. [48] S. McDonald, C. Shen, F. Fillion-Gourdeau, S. Jeon, C. Gale, Hydrodynamic predictions for Pb +Pb collisions at 5.02 A TeV, arXiv:1609.02958 [hep-ph]. [49] CMS Collaboration, V. Khachatryan, et al., Evidence for transverse momentum and pseudorapidity dependent event plane fluctuations in PbPb and pPb collisions, Phys. Rev. C 92 (3) (2015) 034911, arXiv:1503.01692 [nucl-ex]. [50] L.-G. Pang, G.-Y. Qin, V. Roy, X.-N. Wang, G.-L. Ma, Longitudinal decorrelation of anisotropic flows in heavy-ion collisions at the CERN Large Hadron Collider, Phys. Rev. C 91 (4) (2015) 044904, arXiv:1410.8690 [nucl-th]. [51] X. Zhu, Y. Zhou, H. Xu, H. Song, Correlations of flow harmonics in 2.76 A TeV Pb–Pb collisions, Phys. Rev. C 95 (4) (2017) 044902, arXiv:1608.05305 [nucl-th]. ALICE Collaboration S. Acharya139, D. Adamová96, J. Adolfsson34, M.M. Aggarwal 101, G. Aglieri Rinella35, M. Agnello31, N. Agrawal48, Z. Ahammed139, N. Ahmad17, S.U. Ahn 80, S. Aiola 143, A. Akindinov65, S.N. Alam139, J.L.B. Alba114, D.S.D. Albuquerque125, D. Aleksandrov92, B. Alessandro59, R. Alfaro Molina75, A. Alici54,12,27, A. Alkin 3, J. Alme22, T. Alt 71, L. Altenkamper22, I. Altsybeev138, C. Alves Garcia Prado124, M. An7, C. Andrei89, D. Andreou35, H.A. Andrews113, A. Andronic109, V. Anguelov106, C. Anson99, T. Antiˇ ci´ c110, F. Antinori57, P. Antonioli 54, R. Anwar127, L. Aphecetche117, H. Appelshäuser71, S. Arcelli27, R. Arnaldi59, O.W. Arnold 107,36, I.C. Arsene 21, M. Arslandok 106, B. Audurier117, A. Augustinus35, R. Averbeck109, M.D. Azmi17, A. Badalà56, Y.W. Baek 61,79, S. Bagnasco59, R. Bailhache71, R. Bala103, A. Baldisseri76, M. Ball45, R.C. Baral68, A.M. Barbano 26, R. Barbera28, F. Barile 33,53, L. Barioglio26, G.G. Barnaföldi142, L.S. Barnby95,113, V. Barret82, P. Bartalini7, K. Barth35, E. Bartsch71, M. Basile27, N. Bastid82, S. Basu141,139, B. Bathen72, G. Batigne117, A. Batista Camejo82, B. Batyunya78, P.C. Batzing21, I.G. Bearden93, H. Beck106, C. Bedda64, N.K. Behera61, I. Belikov135, F. Bellini 27, H. Bello Martinez2, R. Bellwied127, L.G.E. Beltran 123, V. Belyaev85, G. Bencedi142, S. Beole26, A. Bercuci89, Y. Berdnikov 98, D. Berenyi 142, R.A. Bertens130, D. Berzano35, L. Betev35, A. Bhasin103, I.R. Bhat103, A.K. Bhati101, B. Bhattacharjee44, J. Bhom121, L. Bianchi127, N. Bianchi51, C. Bianchin141, J. Bielˇ cík39, J. Bielˇ cíková96, A. Bilandzic36,107, G. Biro142, R. Biswas4, S. Biswas4, J.T. Blair122, D. Blau92, C. Blume71, G. Boca136, F. Bock 106,84,35, A. Bogdanov85, L. Boldizsár142, M. Bombara40, G. Bonomi137, M. Bonora35, J. Book71, H. Borel76, A. Borissov19, M. Borri129, E. Botta26, C. Bourjau93, P. Braun-Munzinger109, M. Bregant124, T.A. Broker 71, T.A. Browning108, M. Broz39, E.J. Brucken46, E. Bruna59, G.E. Bruno33, D. Budnikov111, H. Buesching71, S. Bufalino31, P. Buhler 116, P. Buncic 35, O. Busch133, Z. Buthelezi77, J.B. Butt15, J.T. Buxton18, J. Cabala119, D. Caffarri35,94, H. Caines143, A. Caliva64, E. Calvo Villar114, P. Camerini25, A.A. Capon116, F. Carena 35, W. Carena 35, F. Carnesecchi27,12, J. Castillo Castellanos76, A.J. Castro130, E.A.R. Casula 24,55, C. Ceballos Sanchez9, P. Cerello59, S. Chandra139, B. Chang128, S. Chapeland35, M. Chartier129, J.L. Charvet76, S. Chattopadhyay139, S. Chattopadhyay 112, A. Chauvin107,36, M. Cherney99, C. Cheshkov 134, B. Cheynis134, V. Chibante Barroso35, D.D. Chinellato125, S. Cho61, P. Chochula 35, K. Choi19, M. Chojnacki93, S. Choudhury139, T. Chowdhury 82, P. Christakoglou94, C.H. Christensen93, P. Christiansen34, T. Chujo 133, S.U. Chung 19, C. Cicalo 55, L. Cifarelli12,27, F. Cindolo 54, J. Cleymans102, F. Colamaria33, D. Colella66,35, A. Collu 84, M. Colocci 27, M. Concas 59,ii, G. Conesa Balbastre83, 76 ALICE Collaboration / Physics Letters B 773 (2017) 68–80 Z. Conesa del Valle 62, M.E. Connors143,iii, J.G. Contreras 39, T.M. Cormier97, Y. Corrales Morales59, I. Cortés Maldonado2, P. Cortese 32, M.R. Cosentino126, F. Costa 35, S. Costanza136, J. Crkovská62, P. Crochet 82, E. Cuautle73, L. Cunqueiro72, T. Dahms 36,107, A. Dainese57, M.C. Danisch106, A. Danu69, D. Das112, I. Das112, S. Das4, A. Dash90, S. Dash48, S. De124,49, A. De Caro30, G. de Cataldo53, C. de Conti124, J. de Cuveland42, A. De Falco24, D. De Gruttola30,12, N. De Marco59, S. De Pasquale30, R.D. De Souza125, H.F. Degenhardt124, A. Deisting109,106, A. Deloff88, C. Deplano94, P. Dhankher48, D. Di Bari33, A. Di Mauro35, P. Di Nezza51, B. Di Ruzza57, M.A. Diaz Corchero 10, T. Dietel 102, P. Dillenseger71, R. Divià 35, Ø. Djuvsland 22, A. Dobrin35, D. Domenicis Gimenez124, B. Dönigus71, O. Dordic21, L.V.V. Doremalen64, T. Drozhzhova71, A.K. Dubey139, A. Dubla109, L. Ducroux134, A.K. Duggal101, P. Dupieux82, R.J. Ehlers143, D. Elia53, E. Endress114, H. Engel 70, E. Epple 143, B. Erazmus117, F. Erhardt 100, B. Espagnon 62, S. Esumi 133, G. Eulisse 35, J. Eum 19, D. Evans113, S. Evdokimov115, L. Fabbietti36,107, J. Faivre83, A. Fantoni51, M. Fasel84,97, L. Feldkamp72, A. Feliciello59, G. Feofilov138, J. Ferencei96, A. Fernández Téllez2, E.G. Ferreiro16, A. Ferretti26, A. Festanti29, V.J.G. Feuillard82,76, J. Figiel121, M.A.S. Figueredo124, S. Filchagin111, D. Finogeev63, F.M. Fionda 24, E.M. Fiore33, M. Floris35, S. Foertsch77, P. Foka 109, S. Fokin92, E. Fragiacomo60, A. Francescon35, A. Francisco117, U. Frankenfeld 109, G.G. Fronze26, U. Fuchs 35, C. Furget83, A. Furs63, M. Fusco Girard30, J.J. Gaardhøje93, M. Gagliardi26, A.M. Gago114, K. Gajdosova93, M. Gallio26, C.D. Galvan123, P. Ganoti 87, C. Gao7, C. Garabatos109, E. Garcia-Solis13, K. Garg28, P. Garg 49, C. Gargiulo35, P. Gasik 107,36, E.F. Gauger122, M.B. Gay Ducati74, M. Germain117, J. Ghosh112, P. Ghosh139, S.K. Ghosh4, P. Gianotti51, P. Giubellino 109,59,35, P. Giubilato29, E. Gladysz-Dziadus121, P. Glässel 106, D.M. Goméz Coral75, A. Gomez Ramirez70, A.S. Gonzalez 35, V. Gonzalez10, P. González-Zamora10, S. Gorbunov42, L. Görlich121, S. Gotovac120, V. Grabski75, L.K. Graczykowski140, K.L. Graham113, L. Greiner84, A. Grelli64, C. Grigoras35, V. Grigoriev85, A. Grigoryan1, S. Grigoryan78, N. Grion60, J.M. Gronefeld109, F. Grosa31, J.F. Grosse-Oetringhaus35, R. Grosso109, L. Gruber116, F. Guber 63, R. Guernane83, B. Guerzoni27, K. Gulbrandsen93, T. Gunji132, A. Gupta103, R. Gupta103, I.B. Guzman2, R. Haake35, C. Hadjidakis62, H. Hamagaki86,132, G. Hamar142, J.C. Hamon135, J.W. Harris143, A. Harton13, H. Hassan83, D. Hatzifotiadou12,54, S. Hayashi132, S.T. Heckel71, E. Hellbär71, H. Helstrup37, A. Herghelegiu89, G. Herrera Corral11, F. Herrmann72, B.A. Hess105, K.F. Hetland37, H. Hillemanns35, C. Hills129, B. Hippolyte135, J. Hladky67, B. Hohlweger107, D. Horak39, S. Hornung109, R. Hosokawa133,83, P. Hristov35, C. Hughes130, T.J. Humanic 18, N. Hussain44, T. Hussain 17, D. Hutter42, D.S. Hwang20, S.A. Iga Buitron73, R. Ilkaev111, M. Inaba133, M. Ippolitov 85,92, M. Irfan17, V. Isakov63, M. Ivanov109, V. Ivanov98, V. Izucheev115, B. Jacak84, N. Jacazio27, P.M. Jacobs 84, M.B. Jadhav48, S. Jadlovska119, J. Jadlovsky119, S. Jaelani64, C. Jahnke36, M.J. Jakubowska140, M.A. Janik 140, P.H.S.Y. Jayarathna127, C. Jena90, S. Jena127, M. Jercic100, R.T. Jimenez Bustamante109, P.G. Jones 113, A. Jusko113, P. Kalinak 66, A. Kalweit35, J.H. Kang 144, V. Kaplin85, S. Kar139, A. Karasu Uysal81, O. Karavichev63, T. Karavicheva63, L. Karayan106,109, E. Karpechev63, U. Kebschull 70, R. Keidel145, D.L.D. Keijdener64, M. Keil35, B. Ketzer45, Z. Khabanova94, P. Khan 112, S.A. Khan139, A. Khanzadeev98, Y. Kharlov 115, A. Khatun17, A. Khuntia49, M.M. Kielbowicz 121, B. Kileng 37, D. Kim144, D.W. Kim 43, D.J. Kim128, H. Kim144, J.S. Kim43, J. Kim106, M. Kim61, M. Kim144, S. Kim20, T. Kim 144, S. Kirsch42, I. Kisel42, S. Kiselev65, A. Kisiel140, G. Kiss 142, J.L. Klay6, C. Klein 71, J. Klein 35, C. Klein-Bösing 72, S. Klewin106, A. Kluge35, M.L. Knichel106, A.G. Knospe127, C. Kobdaj118, M. Kofarago142, T. Kollegger109, A. Kolojvari138, V. Kondratiev138, N. Kondratyeva85, E. Kondratyuk115, A. Konevskikh63, M. Konyushikhin141, M. Kopcik119, M. Kour 103, C. Kouzinopoulos35, O. Kovalenko88, V. Kovalenko138, M. Kowalski 121, G. Koyithatta Meethaleveedu48, I. Králik66, A. Kravˇ cáková 40, M. Krivda 66,113, F. Krizek 96, E. Kryshen98, M. Krzewicki42, A.M. Kubera18, V. Kuˇ cera96, C. Kuhn135, P.G. Kuijer 94, A. Kumar103, J. Kumar48, L. Kumar 101, S. Kumar48, S. Kundu90, P. Kurashvili88, A. Kurepin63, A.B. Kurepin63, A. Kuryakin111, S. Kushpil96, M.J. Kweon 61, Y. Kwon 144, S.L. La Pointe42, P. La Rocca28, C. Lagana Fernandes124, Y.S. Lai 84, I. Lakomov35, R. Langoy41, K. Lapidus143, C. Lara 70, A. Lardeux76,21, A. Lattuca26, E. Laudi35, R. Lavicka39, L. Lazaridis35, R. Lea25, L. Leardini106, S. Lee144, F. Lehas94, S. Lehner116, J. Lehrbach42, R.C. Lemmon95, V. Lenti53, E. Leogrande 64, I. León Monzón123, P. Lévai 142, S. Li7, X. Li14, J. Lien41, R. Lietava113, B. Lim19, S. Lindal21, V. Lindenstruth42, S.W. Lindsay129, C. Lippmann109, M.A. Lisa 18, V. Litichevskyi46, H.M. Ljunggren34, W.J. Llope 141, D.F. Lodato64,