Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at √sNN=2.76 TeV

JHEP09(2016)164 Published for SISSA by Springer Received:July 6, 2016 Revised:August 30, 2016 Accepted:September 20, 2016 Published:September 28, 2016 Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at √sNN = 2.76 TeV The ALICE collaboration E-mail: [email protected] Abstract: The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for π±, K±and p+p in Pb-Pb collisions at √sNN = 2.76 TeV were measured with the ALICE detector at the Large Hadron Collider. The results were obtained with the Scalar Product method, correlating the identified hadrons with reference particles from a different pseudorapidity region. Effects not related to the common event symmetry planes (non-flow) were estimated using correlations in pp collisions and were subtracted from the measurement. The obtained flow coefficients exhibit a clear mass ordering for transverse momentum (pT) values below ≈3 GeV/c. In the intermediate pTregion (3 < pT<6 GeV/c), particles group at an approximate level according to the number of constituent quarks, suggesting that coalescence might be the relevant particle production mechanism in this region. The results for pT<3 GeV/care described fairly well by a hydrodynamical model (iEBE-VISHNU) that uses initial conditions generated by A Multi-Phase Transport model (AMPT) and describes the expansion of the fireball using a value of 0.08 for the ratio of shear viscosity to entropy density (η/s), coupled to a hadronic cascade model (UrQMD). Finally, expectations from AMPT alone fail to quantitatively describe the measurements for all harmonics throughout the measured transverse momentum region. However, the comparison to the AMPT model highlights the importance of the late hadronic rescattering stage to the development of the observed mass ordering at low values of pTand of coalescence as a particle production mechanism for the particle type grouping at intermediate values of pTfor all harmonics. Keywords: Hadron-Hadron scattering (experiments) ArXiv ePrint: 1606.06057 Open Access, Copyright CERN, for the benefit of the ALICE Collaboration. Article funded by SCOAP3. doi:10.1007/JHEP09(2016)164 JHEP09(2016)164 Contents 1 Introduction 1 2 Experimental setup 3 3 Event sample, track selection and particle identification 4 3.1 Trigger selection and data sample 4 3.2 Track selection 5 3.3 Identification of π±,K±and p+p 6 4 Analysis technique 7 4.1 Scalar Product method 7 4.2 Estimation of non-flow correlations 8 5 Systematic uncertainties 9 6 Results and discussion 12 6.1 Centrality dependence of flow harmonics 12 6.2 Evolution of flow harmonics in ultra-central Pb-Pb collisions 16 6.3 Mass ordering 16 6.4 Test of scaling properties 19 6.5 Comparison with models 21 6.5.1 Comparison with iEBE-VISHNU 21 6.5.2 Comparison with AMPT 23 7 Conclusions 25 A Additional figures 28 A.1 Integrated vn28 A.2 NCQ scaling 29 A.3 KETscaling 30 The ALICE collaboration 36 1 Introduction Quantum chromodynamics (QCD) calculations on the lattice [1,2] suggest that at high values of temperature and energy density a transition takes place from ordinary nuclear matter to a state where the constituents, the quarks and the gluons, are deconfined. This state of matter is called the quark-gluon plasma (QGP) [3–5]. The aim of the heavy-ion – 1 – JHEP09(2016)164 program at the Large Hadron Collider (LHC) is to study the QGP properties, such as the equation of state, the speed of sound in the medium, and the value of the ratio of shear viscosity to entropy density (η/s). One of the important observables sensitive to the properties of the QGP is the azimuthal distribution of particles emitted in the plane transverse to the beam direction. In non-central collisions between two heavy ions the overlap region is not isotropic. This spatial anisotropy of the overlap region is transformed into an anisotropy in momentum space initially through interactions between partons and at later stages between the produced particles. The resulting anisotropy is usually expressed in terms of a Fourier series in azimuthal angle ϕ[6,7] according to Ed3N dp3=1 2π d2N pTdpTdη1+2 ∞ X n=1 vn(pT, η) cos[n(ϕ−Ψn)],(1.1) where E,N,p,pT,ϕand ηare the energy, particle yield, total momentum, transverse momentum, azimuthal angle and pseudorapidity of particles, respectively, and Ψnis the azimuthal angle of the symmetry plane of the nth-order harmonic [8–11]. The nth-order flow coefficients are denoted as vnand can be calculated as vn=hcos[n(ϕ−Ψn)]i,(1.2) where the brackets denote an average over all particles in all events. Since the symmetry planes are not accessible experimentally, the flow coefficients are estimated solely from the azimuthal angles of the produced particles. The second Fourier coefficient, v2, measures the elliptic flow, i.e. the momentum space azimuthal anisotropy of particle emission relative to the second harmonic symmetry plane. The study of v2at both the Relativistic Heavy Ion Collider (RHIC) and the LHC contributed significantly to the realisation that the produced system can be described as a strongly-coupled quark-gluon plasma (sQGP) with a small value of η/s, very close to the conjectured lower limit of 1/4πfrom AdS/CFT [12]. In addition, the overlap region of the colliding nuclei exhibits an irregular shape [8–11,13]. The irregularities originate from the initial density profile of nucleons participating in the collision, which is not isotropic and differs from one event to the other. This, in turn, causes the symmetry plane of the irregular shape to fluctuate in every event around the reaction plane, defined by the impact parameter vector and the beam axis, and also gives rise to the additional higher harmonic symmetry planes Ψn. The initial state fluctuations yield higher order flow harmonics such as v3,v4, and v5that are usually referred to as triangular, quadrangular, and pentagonal flow, respectively. Recent calculations [14,15] suggest that their transverse momentum dependence is a more sensitive probe than elliptic flow not only of the initial geometry and its fluctuations, but also of η/s. The first measurements of the pT-differential vn, denoted as vn(pT), of charged particles at the LHC [16–18] provided a strong testing ground for hydrodynamical calculations that attempt to describe the dynamical evolution of the system created in heavy-ion collisions. An additional challenge for hydrodynamical calculations and a constraint on both the initial conditions and η/s can be provided by studying the flow coefficients of eq. (1.2) as – 2 – JHEP09(2016)164 a function of collision centrality and transverse momentum for different particle species. The first results of such studies at RHIC [19–22] and the LHC [23,24] revealed that an interplay of radial flow (the average velocity of the system’s collective radial expansion) and anisotropic flow leads to a characteristic mass dependence of v2(pT) [25–27] for pT<3 GeV/c. For higher values of transverse momentum up to pT≈6 GeV/cthese results indicate that the v2of baryons is larger than that of mesons. This behaviour was explained in a dynamical model where flow develops at the partonic level followed by quark coalescence into hadrons [28,29]. This mechanism leads to the observed hierarchy in the values of v2(pT), referred to as number of constituent quarks (NCQ) scaling. New results from ALICE [23] and PHENIX [30] exhibit deviations from the NCQ scaling at the level of ±20% for pT>3 GeV/c. In addition, the LHC results showed also that the v2of the φ-meson at intermediate values of transverse momentum follows the baryon rather than the meson scaling for central Pb-Pb collisions [23]. Recently, the first results of v2(pT), v3(pT), and v4(pT) for π±, K±and p+p for 50% most central Au-Au collisions at √sNN = 200 GeV were reported [31]. The higher harmonic flow coefficients exhibit similar mass and particle-type dependences as v2up to intermediate values of pT. In this article, we report the results for the pT-differential elliptic, triangular, quadrangular and pentagonal flow for π±, K±and p+p measured in Pb-Pb collisions at the centre of mass energy per nucleon pair √sNN = 2.76 TeV with the ALICE detector [32,33] at the LHC. The particles are identified using signals from both the Time Projection Chamber (TPC) and the Time Of Flight (TOF) detectors, described in section 2, with a procedure that is discussed in section 3. The results are obtained with the Scalar Product method described in section 4, and in detail in refs. [23,34–36]. In this article, the identified hadron under study and the charged reference particles are obtained from different, non-overlapping pseudorapidity regions. A correction for correlations not related to the common symmetry plane (non-flow), like those arising from jets, resonance decays and quantum statistics correlations, is presented in section 4. This procedure relies on measuring the corresponding correlations in pp collisions and subtracting them from the vncoefficients measured in Pb-Pb collisions to form the reported vsub n(pT), where the superscript ‘sub’ is used to stress the subtraction procedure. The systematic uncertainties of the measurements are described in section 5. All harmonics were measured separately for particles and anti-particles and were found to be compatible within the statistical uncertainties. Therefore, the vsub n(pT) for the average of the results for the opposite charges is reported. The results are reported in section 6for the 0–50% centrality range of Pb-Pb collisions. Finally, results are also reported separately for ultra-central events, i.e. the 0–1% centrality range, where the role of the collision geometry is reduced and one expects that vsub n(pT) is mainly driven by the initial state fluctuations. 2 Experimental setup ALICE [32,33] is one of the four large experiments at the LHC, particularly designed to cope with the large charged-particle densities present in central Pb-Pb collisions [37]. By convention, the beam direction defines the z-axis, the x-axis is horizontal and points – 3 – JHEP09(2016)164 towards the centre of the LHC, and the y-axis is vertical and points upwards. The apparatus consists of a set of detectors located in the central barrel, positioned inside a solenoidal magnet which generates a 0.5 T field parallel to the beam direction, and a set of forward detectors. The Inner Tracking System (ITS) [32] and the TPC [38] are the main tracking detectors of the central barrel. The ITS consists of six layers of silicon detectors employing three different technologies. The two innermost layers, positioned at r= 3.9 cm and 7.6 cm, are Silicon Pixel Detectors (SPD), followed by two layers of Silicon Drift Detectors (SDD) (r= 15 cm and 23.9 cm). Finally, the two outermost layers are double-sided Silicon Strip Detectors (SSD) at r= 38 cm and 43 cm. The TPC surrounds the ITS and provides full azimuthal coverage in the pseudorapidity range |η|<0.9. Charged pions, kaons and protons were identified using the information from the TPC and the TOF detectors [32]. The TPC allows for a simultaneous measurement of the momentum of a particle and its specific energy loss hdE/dxiin the gas. The detector provides a separation by at least 2 standard deviations for the hadron species at pT<0.7 GeV/cand the possibility to identify particles in the relativistic rise region of dE/dx(i.e. 2 < pT<20 GeV/c) [33]. The dE/dxresolution for the 5% most central Pb-Pb collisions is 6.5% and improves for more peripheral collisions. The TOF detector is placed around the TPC and provides a 3σseparation between π-K and K-p up to pT= 2.5 GeV/cand pT= 4 GeV/c, respectively [33]. This is done by measuring the flight time of particles from the collision point with a resolution of about 80 ps. The start time for the TOF measurement is provided by the T0 detectors, two arrays of Cherenkov counters positioned at opposite sides of the interaction points covering 4.6< η < 4.9 (T0A) and −3.3< η < −3.0 (T0C). The start time is also determined using a combinatorial algorithm that compares the timestamps of particle hits measured by the TOF to the expected times of the tracks, assuming a common event time tev [33]. Both methods of estimating the start time are fully efficient for the 50% most central Pb-Pb collisions. A set of forward detectors, the V0 scintillator arrays [39], were used in the trigger logic and for the determination of the collision centrality, discussed in the next section. The V0 consists of two systems, the V0A and the V0C, that are positioned on each side of the interaction point and cover the pseudorapidity ranges of 2.8< η < 5.1 and −3.7< η < −1.7, respectively. For more details on the ALICE experimental setup and the performance of the detectors, see refs. [32,33]. 3 Event sample, track selection and particle identification 3.1 Trigger selection and data sample The analysis is performed on data from pp and Pb-Pb collisions at √sNN = 2.76 TeV collected with the ALICE detector in 2011. The minimum bias trigger in pp collisions required at least one hit in either of the V0 detectors or the SPD. In Pb-Pb collisions, minimum bias events were triggered by the coincidence between signals from the two sides of the V0 detector. In addition, in Pb-Pb collisions, an online selection based on the – 4 – JHEP09(2016)164 V0 detectors was used to increase the number of central (i.e. 0–10% centrality range) and semi-central (i.e. 10–50% centrality range) events. An offline event selection, exploiting the signal arrival time in V0A and V0C, measured with a 1 ns resolution, was used to discriminate background (e.g. beam-gas) from collision events. This led to a reduction of background events in the analysed samples to a negligible fraction (<0.1%) [33]. All events selected for the analysis had a reconstructed primary vertex position along the beam axis (zvtx) within 10 cm from the nominal interaction point. Finally, events with multiple reconstructed vertices were rejected, leading to a negligible amount of pile-up events for all systems [33]. After all the selection criteria, a filtered data sample of approximately 25 ×106Pb-Pb and 20 ×106pp events were analysed to produce the results presented in this article. Events were classified according to fractions of the inelastic cross section and correspond to the 50% most central Pb-Pb collisions. The 0–1% interval represents the most central interactions (i.e. smallest impact parameter) and will be referred to as ultra-central collisions in the following. On the other hand, the 40–50% interval corresponds to the most peripheral (i.e. largest impact parameter) collisions in the analysed sample, imposed by the usage of the semi-central trigger for the collected sample in 2011. The centrality of the collision was estimated using the distribution of signal amplitudes from the V0 detectors. The systematic uncertainty due to the centrality estimation is determined using the charged particle multiplicity distribution of TPC tracks and the number of SPD clusters, and will be discussed in section 5. Details about the centrality determination can be found in ref. [40]. 3.2 Track selection In this analysis, tracks are reconstructed using the information from the TPC and the ITS detectors. The tracking algorithm, based on the Kalman filter [41,42], starts from a collection of space points (referred to as clusters) inside the TPC, and provides the quality of the fit by calculating its χ2value. Each space point is reconstructed at one of the TPC padrows, where the deposited ionisation energy is also measured. The specific ionisation energy loss hdE/dxiis estimated using a truncated mean, excluding the 40% highest-charge clusters associated to the track. The obtained hdE/dxihas a resolution, which we later refer to as σTPC. The tracks are propagated to the outer layer of the ITS, and the tracking algorithm attempts to identify space points in each one of the consecutive layers, reaching the innermost ones (i.e. SPD). The track parameters are then updated using the combined information from both the TPC and the ITS detectors. If the algorithm is unable to match the track reconstructed in the TPC with associated ITS clusters (e.g. due to inefficiencies caused by dead channels in some of the ITS layers), the track parameters calculated from the TPC tracking algorithm are used instead. This tracking mode will be referred to as hybrid tracking in the rest of the text, and is used as the default in this analysis since it also provides uniform ϕdistribution. Primary charged pions, kaons and (anti-)protons were required to have at least 70 reconstructed space points out of the maximum of 159 in the TPC. The average χ2of the track fit per TPC space point per degree of freedom (see [33] for details) was required – 5 – JHEP09(2016)164 to be below 2. These selections reduce the contribution from short tracks, which are unlikely to originate from the primary vertex. To further reduce the contamination by secondary tracks from weak decays or from the interaction with the material, only particles within a maximum distance of closest approach (DCA) between the tracks and the primary vertex in both the transverse plane (DCAxy <2.4 cm) and the longitudinal direction (DCAz<3.2 cm) were analysed. Moreover, the tracks were required to have at least two associated ITS clusters in addition to having a hit in either of the two SPD layers. This selection leads to an efficiency of about 80% for primary tracks at pT>0.6 GeV/cand a contamination from secondaries of about 5% at pT= 1 GeV/c[43]. These values depend on particle species and transverse momentum [43]. The systematic uncertainty due to the track reconstruction mode was estimated using two additional tracking modes, one relying on the so-called standalone TPC tracking with the same parameters described before, and a second that relies on the combination of the TPC and the ITS detectors (i.e. global tracking) with tighter selection criteria. In the latter case, the maximum value of DCA was 0.3 cm in both the transverse plane and the longitudinal direction, thus further reducing the amount of secondary particles in the track sample. The results are reported for all identified hadrons in |η|<0.8 and for the transverse momentum range 0.3< pT<6.0 GeV/c for π±and 0.3< pT<4.0 GeV/c for K±. Finally, since the contamination from secondary protons created through the interaction of particles with the detector material can reach values larger than 5% for pT<1 GeV/c, only p were considered for 0.4< pT<1 GeV/c, while for higher values (i.e. 1 < pT<6 GeV/c) a combined measurement of p and p is reported. 3.3 Identification of π±,K±and p+p The particle identification (PID) for pions (π±), kaons (K±) and protons (p+p) used in this analysis is based on a Bayesian technique described in detail in [44], with the time-of-flight tTOF and the specific energy loss in the TPC hdE/dxias the input quantities. Different particle species are identified by requiring a minimum probability of 90%. The PID efficiency of this method is higher than 95% both for pions and protons up to pT≈2.5 GeV/c while for kaons it exhibits a stronger pTdependence, reaching 60% at 2.5 GeV/c with a minimum of 25% at 4 GeV/c. Furthermore, the contamination is below 5% both for pions and protons, while for kaons it remains below 10% throughout the entire transverse momentum range considered in this analysis. In addition, a different PID procedure that relied on the two-dimensional correlation between the number of standard deviations in units of the resolution from the expected signals of the TPC and the TOF detectors was also investigated, similar to what was reported in [23]. In this approach particles were selected by requiring their signal to lie within maximum three standard deviations from the hdE/dxiand tTOF values expected for a given particle species and transverse momentum. In addition, the purity was required to be at least 80%, a condition that becomes essential with increasing transverse momentum where the relevant detector response for different particle species starts to overlap. – 6 – JHEP09(2016)164 4 Analysis technique In this article, higher flow harmonics for charged pions, charged kaons, protons and antiprotons are reported. In the following paragraphs, the technique used for the measurement of flow harmonics is discussed and an approach to estimate the contribution of non-flow correlations, applied to obtain the final results, is presented. For the estimation of these higher flow harmonics, the symmetry planes are not reconstructed on an event-by-event basis and thus the azimuthal angles of particles are not directly correlated to them. Instead, they are estimated with correlation techniques, where only the azimuthal angles of produced particles are required. 4.1 Scalar Product method In this article, the flow harmonics are calculated with the Scalar Product (SP) method [34,35] in which the identified particle of interest (POI) and the charged reference particles (RP) are both selected within the acceptance of the TPC detector. This method is based on the calculation of the Q-vector from a sample of RP [45], according to ~ Qn= M X k∈RP einϕk,(4.1) where Mis the multiplicity of RPs, ϕkis the azimuthal angle of the kth reference particle and nis the order of the flow harmonic. In this study, each event is divided into two subevents “a” and “b”, covering the ranges −0.8< η < 0.0 and 0.0< η < 0.8, respectively. The measured va n(vb n) coefficients are calculated by selecting the identified hadrons (POIs) from subevent “a” (“b”) and the reference particles from subevent “b” (“a”) according to va n(pT) = DD~uk n(pT)·~ Qb∗ n MbEk∈aE rD~ Qa n Ma·~ Qb∗ n MbE .(4.2) In eq. (4.2), the brackets denote an average over all particles and all events, Maand Mb are the measured multiplicities of RPs from each subevent in the TPC detector, ~uk n=einϕk, k∈a, is the unit vector of the kth POI in subevent “a”, ~ Qa nis the Q-vector calculated in subevent “a” and ~ Qb∗ nis the complex conjugate of the Q-vector calculated in subevent “b”. The denominator in eq. (4.2) is referred to further in the text as reference flow. The final measured vAA ncoefficients are calculated as a weighted average of va nand vb nwith the inverse of the square of the statistical uncertainty being the weight. The Scalar Product method, used in this article, as well as in [23], requires less statistics than multi-particle methods, since it is essentially based on two-particle correlations. In addition, it does not introduce any bias originating from multiplicity fluctuations since all Q-vectors in eq. (4.2) are normalised by the relevant multiplicities [36]. – 7 – JHEP09(2016)164 4.2 Estimation of non-flow correlations Even after selecting particles from two non-overlapping subevents, a significant residual non-flow contribution remains in the measured flow coefficients. These non-flow contributions are mainly few-particle effects and scale roughly with the inverse of the multiplicity for methods which rely on two-particle correlations, such as the SP. These include correlations originating from jets, resonance decays and quantum statistics correlations which contribute additively to the value of vAA n. We assume that they do not drastically change with the centrality interval, as discussed in [35,46] and shown in [47]. The corresponding contributions can be estimated using minimum bias pp collisions [35] and in this article this estimate, denoted as δAA,pp n, is subtracted from the measured flow coefficients according to vsub n(pT) = vAA n(pT)−δAA,pp n(pT),(4.3) δ(a)AA,pp n(pT) = hMippDD~uk n(pT)·~ Qb∗ n MbEk∈aEpp hMiAArD~ Qa n Ma·~ Qb∗ n MbEAA ,(4.4) where the final δAA,pp nis calculated as a weighted average of δ(a)AA,pp nand δ(b)AA,pp nwith the inverse of the square of the statistical uncertainty as the weight. The term δ(a)AA,pp nis given by eq. (4.4) (similarly for δ(b)AA,pp n). In eq. (4.4), hMipp and hMiAA are the average multiplicities of RPs calculated in pp and Pb-Pb collisions, respectively. In this article, we report the results of vsub n, defined in eq. (4.3), with the superscript ‘sub’ added to stress the applied subtraction procedure. This approach is different compared to previous measurements [23,48], where a large pseudorapidity gap ∆ηbetween the POIs and the RPs was used to significantly reduce the contribution from non-flow correlations. The vsub 2results reported in this article are 2–6% below the v2measurements reported in [23]. This is probably due to the fact that the subtraction procedure using pp collisions accounts for the recoil (away-side) jet which is not accounted for by applying a large η-gap. On the other hand, it does not account for known medium-induced modifications of jet-like correlations. This could lead to an over-estimation of the non-flow component in high pTvalues. Figure 1presents the pT-differential hMihh~un·~ Q∗ n Mii, i.e. the azimuthal correlations scaled by the relevant multiplicities, in pp and Pb-Pb in three centrality intervals (i.e. 0– 1%, 20–30% and 40–50%) for all flow harmonics reported in this article for pions, kaons and protons, in the appropriate kinematic range for each species. The data points are drawn with statistical and systematic uncertainties, represented by the error bars and the boxes, respectively. This representation is used in all plots of this article. It is seen that hMipphh~u2·~ Q∗ 2 Miipp increases monotonically with pT, reaching the magnitude of hMiAAhh~u2·~ Q∗ 2 MiiAA in ultra-central collisions at high values of pT, where non-flow correlations are expected to become significant. – 8 – JHEP09(2016)164 1 2 3 4 5 6 sub 4 v 0 0.05 0.1 0.15 ± π =2.76 TeV NN sALICE Pb-Pb )c (GeV/ T p 1 2 3 4 5 6 4 AA,pp δ 0 0.02 0.04 0.06 1 2 3 4 5 6 0 0.05 0.1 0.15 ± K )c (GeV/ T p 1 2 3 4 5 6 0 0.02 0.04 0.06 Centrality intervals 0-1% 0-5% 5-10% 10-20% 20-30% 30-40% 40-50% 1 2 3 4 5 6 0 0.05 0.1 0.15 pp+ )c (GeV/ T p 1 2 3 4 5 6 0 0.02 0.04 0.06 Figure 4. The pT-differential vsub 4(top row) and δAA,pp 4(bottom row) for different centralities in Pb-Pb collisions at √sNN = 2.76 TeV grouped by particle species. 1 2 3 4 5 6 sub 5 v 0 0.05 0.1 ± π =2.76 TeV NN sALICE Pb-Pb )c (GeV/ T p 1 2 3 4 5 6 5 AA,pp δ 0 0.02 0.04 0.06 1 2 3 4 5 6 0 0.05 0.1 ± K )c (GeV/ T p 1 2 3 4 5 6 0 0.02 0.04 0.06 Centrality intervals 0-1% 0-5% 5-10% 10-20% 20-30% 30-40% 40-50% 1 2 3 4 5 6 0 0.05 0.1 pp+ )c (GeV/ T p 1 2 3 4 5 6 0 0.02 0.04 0.06 Figure 5. The pT-differential vsub 5(top row) and δAA,pp 5(bottom row) for different centralities in Pb-Pb collisions at √sNN = 2.76 TeV grouped by particle species. – 15 – JHEP09(2016)164 6.2 Evolution of flow harmonics in ultra-central Pb-Pb collisions Figure 6shows the evolution of different flow harmonics for π±(left column), K±(middle column) and p+p (right column) for ultra-central (i.e. 0–1%) collisions in comparison to the other centrality intervals. For ultra-central Pb-Pb collisions one expects the influence of the collision geometry to the development of vsub nto be reduced compared to the contribution of initial energydensity fluctuations. Figure 6shows that for pions the value of vsub 3is equal to vsub 2at around pT≈1 GeV/c and becomes the dominant harmonic for higher transverse momenta. Furthermore, vsub 4at pT≈2 GeV/c and vsub 5at around pT≈3 GeV/c become equal to vsub 2. For higher transverse momentum values, vsub 4becomes gradually larger than vsub 2reaching a similar magnitude as vsub 3at around 3.5 GeV/c, while vsub 5remains equal to vsub 2. As the collisions become more peripheral, one expects that geometry becomes a significant contributor to the development of azimuthal anisotropy. As a result, vsub 2is the dominant harmonic for peripheral collisions throughout the entire measured momentum range. Furthermore, vsub 3,vsub 4and vsub 5seem to have similar magnitudes and pTevolution as observed in ultra-central Pb-Pb events, indicating a smaller influence of the collision geometry in their development than for vsub 2. For kaons and protons, one observes a similar trend in the pTevolution of vsub 2,vsub 3, vsub 4and vsub 5as for pions. However, the flow harmonics for ultra-central collisions (top middle and right plots of figure 6respectively) exhibit a crossing that takes place at pTvalues that change as a function of the particle mass. For kaons, the crossing between vsub 2and vsub 3occurs at higher pT(≈1.4 GeV/c) compared to pions while for protons it occurs at an even higher pTvalue (≈1.8 GeV/c). Similarly, the vsub 2and vsub 4crossing occurs higher in pTfor kaons (≈2.2 GeV/c) and protons (≈2.8 GeV/c) as compared to pions. The values of vsub 4for kaons reach a similar magnitude to vsub 3at around 3.5 GeV/c and this takes place at around 4 GeV/c for protons. The dependence of the crossing between different flow harmonics, and thus the range where a given harmonic becomes dominant, on the particle mass can be attributed to the interplay of not only elliptic but also triangular and quadrangular flow with radial flow. 6.3 Mass ordering The interplay between the different flow harmonics and radial flow can be further probed by studying how vsub n(pT) develops as a function of the particle mass for various centralities. In ref. [23], it was clearly demonstrated that the interplay between radial and elliptic flow leads to a characteristic mass ordering at pT<2–3 GeV/c. This mass ordering originates from the fact that radial flow creates a depletion in the particle spectrum at low pTvalues, which increases with increasing particle mass and transverse velocity. When this effect is embedded in an environment where azimuthal anisotropy develops, it leads to heavier particles having smaller vsub nvalues compared to lighter ones at given values of pT. It is thus interesting to study whether the interplay between the anisotropic flow harmonics and radial flow leads also to a mass ordering in vsub n(pT) for n > 2. – 16 – JHEP09(2016)164 1 2 3 4 5 0 0.05 0.1 ± π 0-1% 1 2 3 4 5 0 0.05 0.1 ± π 0-5% 1 2 3 4 5 0 0.05 0.1 0.15 ± π 5-10% 1 2 3 4 5 sub n v 0 0.1 0.2 ± π 10-20% 1 2 3 4 5 0 0.1 0.2 0.3 ± π 20-30% 1 2 3 4 5 0 0.1 0.2 0.3 ± π 30-40% 1 2 3 4 5 0 0.1 0.2 0.3 ± π 40-50% 1 2 3 4 5 0 0.05 0.1 ± K =2.76 TeV NN s ALICE Pb-Pb sub 2 v sub 3 v sub 4 v sub 5 v 1 2 3 4 5 0 0.05 0.1 ± K 1 2 3 4 5 0 0.05 0.1 0.15 ± K 1 2 3 4 5 0 0.1 0.2 ± K 1 2 3 4 5 0 0.1 0.2 0.3 ± K 1 2 3 4 5 0 0.1 0.2 0.3 ± K )c (GeV/ T p 1 2 3 4 5 0 0.1 0.2 0.3 ± K 1 2 3 4 5 0 0.05 0.1 pp+ 1 2 3 4 5 0 0.05 0.1 pp+ 1 2 3 4 5 0 0.05 0.1 0.15 pp+ 1 2 3 4 5 0 0.1 0.2 pp+ 1 2 3 4 5 0 0.1 0.2 0.3 pp+ 1 2 3 4 5 0 0.1 0.2 0.3 pp+ 1 2 3 4 5 0 0.1 0.2 0.3 pp+ Figure 6. The evolution of the pT-differential vsub nfor π±, K±and p+p, in the left, middle and right columns, respectively, grouped by centrality interval in Pb-Pb collisions at √sNN = 2.76 TeV. – 17 – JHEP09(2016)164 sub 2 v 0 0.05 0-1% sub 2 v 0 0.05 0.1 0.15 0-5% sub 2 v 0 0.1 0.2 10-20% )c (GeV/ T p 1 2 3 4 5 sub 2 v 0 0.1 0.2 0.3 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0 0.05 0.1 0.15 5-10% 0 0.1 0.2 20-30% )c (GeV/ T p 1 2 3 4 5 0 0.1 0.2 0.3 40-50% sub 3 v 0 0.05 0.1 0-1% sub 3 v 0 0.05 0.1 0.15 0-5% sub 3 v 0 0.05 0.1 0.15 10-20% )c (GeV/ T p 1 2 3 4 5 sub 3 v 0 0.05 0.1 0.15 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0 0.05 0.1 0.15 5-10% 0 0.05 0.1 0.15 20-30% )c (GeV/ T p 1 2 3 4 5 0 0.05 0.1 0.15 40-50% Figure 7. The pT-differential vsub 2(left figure) and vsub 3(right figure) for different particle species grouped by centrality class in Pb-Pb collisions at √sNN = 2.76 TeV. Figure 7–left presents the pT-differential vsub 2for charged pions, kaons and protons starting from ultra-central collisions up to the 40–50% centrality interval. The observed evolution of vsub 2with mass confirms that the interplay between elliptic and radial flow leads to lower vsub 2values at fixed pTfor heavier particles for pT<2–3 GeV/c, depending on the centrality interval. Similarly, figures 7–right, 8–left and 8–right show the pT-differential vsub 3,vsub 4and vsub 5, respectively, for different particle species and for each centrality interval. A clear mass ordering is seen in the low pTregion, i.e. for pT<2–3 GeV/c, for vsub 3(pT), vsub 4(pT) and vsub 5(pT), which arises from the interplay between the anisotropic flow harmonics and radial flow. Furthermore, the vsub n(pT) values show a crossing between pions, kaons and protons, that, depending on the centrality and the order of the flow harmonic, takes place at different pTvalues. In figures 7and 8it is seen that the crossing between, e.g. π±and p+p occurs at lower pTfor more peripheral collisions in comparison to more central events. The crossing point for central collisions occurs at higher pTvalues for vsub nsince the common velocity field, which exhibits a significant centrality dependence, affects heavy particles more. The current study shows that this occurs not only in the case of elliptic flow but also for higher flow harmonics. Finally, beyond the crossing point for each centrality and for every harmonic, it is seen that particles tend to group based on their number of constituent quarks. This apparent grouping will be discussed in the next subsection. – 18 – JHEP09(2016)164 sub 4 v 0 0.05 0.1 0-1% sub 4 v 0 0.05 0.1 0-5% sub 4 v 0 0.05 0.1 0.15 10-20% )c (GeV/ T p 1 2 3 4 5 sub 4 v 0 0.05 0.1 0.15 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0 0.05 0.1 5-10% 0 0.05 0.1 0.15 20-30% )c (GeV/ T p 1 2 3 4 5 0 0.05 0.1 0.15 40-50% sub 5 v 0 0.05 0.1 0-1% sub 5 v 0 0.05 0.1 0-5% sub 5 v 0 0.05 0.1 10-20% )c (GeV/ T p 1 2 3 4 5 sub 5 v 0 0.05 0.1 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0 0.05 0.1 5-10% 0 0.05 0.1 20-30% )c (GeV/ T p 1 2 3 4 5 0 0.05 0.1 40-50% Figure 8. The pT-differential vsub 4(left figure) and vsub 5(right figure) for different particle species grouped by centrality class in Pb-Pb collisions at √sNN = 2.76 TeV. 6.4 Test of scaling properties It was first observed at RHIC that at intermediate values of transverse momentum (3 < pT<6 GeV/c) the value of v2for baryons is larger than that of mesons [19–22]. As a result it was suggested that if both vnand pTare scaled by the number of constituent quarks (nq), the resulting pT/nqdependence of the scaled values for all particle species will have an approximate similar magnitude and dependence on scaled transverse momentum. This scaling, known as number of constituent quark scaling (NCQ), worked fairly well at RHIC energies, although later measurements revealed sizeable deviations from a perfect scaling [30]. Recently, ALICE measurements [23] showed that the NCQ scaling at LHC energies holds at an approximate level of ±20% for vAA 2. Although the scaling is only approximate, it stimulated various theoretical ideas that attempted to address its origin. As a result, several models [28,29] attempted to explain this observed effect by requiring quark coalescence to be the dominant particle production mechanism in the intermediate pTregion, where the hydrodynamic evolution of the fireball is not the driving force behind the development of anisotropic flow. Figures 9and 10 present vsub 2and vsub 3, as well as vsub 4and vsub 5, respectively, scaled by the number of constituent quarks (nq) as a function of pT/nqfor π±, K±and p+p grouped in centrality bins. Figure 9–left is consistent with the observation reported in [23] related to the elliptic flow. For higher harmonics this scaling holds at the same level (±20%) within the current statistical and systematic uncertainties. – 19 – JHEP09(2016)164 0.5 1 1.5 2 2.5 q n/ sub 2 v 0 0.01 0.02 0.03 0-1% 0.5 1 1.5 2 2.5 q n/ sub 2 v 0 0.02 0.04 0.06 0-5% 0.5 1 1.5 2 2.5 q n/ sub 2 v 0 0.05 0.1 10-20% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 q n/ sub 2 v 0 0.05 0.1 0.15 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 5-10% 0.5 1 1.5 2 2.5 0 0.05 0.1 20-30% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 0 0.05 0.1 0.15 40-50% q n/ sub 3 v 0 0.02 0.04 0.06 0-1% q n/ sub 3 v 0 0.02 0.04 0.06 0-5% q n/ sub 3 v 0 0.02 0.04 0.06 10-20% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 q n/ sub 3 v 0 0.02 0.04 0.06 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0 0.02 0.04 0.06 5-10% 0 0.02 0.04 0.06 20-30% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 40-50% Figure 9. The pT/nqdependence of vsub 2/nq(left figure) and vsub 3/nq(right figure) for π±, K±and p+p for Pb-Pb collisions in various centrality intervals at √sNN = 2.76 TeV. 0.5 1 1.5 2 2.5 q n/ sub 4 v 0 0.02 0.04 0.06 0-1% 0.5 1 1.5 2 2.5 q n/ sub 4 v 0 0.02 0.04 0.06 0-5% 0.5 1 1.5 2 2.5 q n/ sub 4 v 0 0.02 0.04 0.06 10-20% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 q n/ sub 4 v 0 0.02 0.04 0.06 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 5-10% 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 20-30% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 0 0.02 0.04 0.06 40-50% 0.5 1 1.5 2 2.5 q n/ sub 5 v 0 0.02 0.04 0-1% 0.5 1 1.5 2 2.5 q n/ sub 5 v 0 0.02 0.04 0-5% 0.5 1 1.5 2 2.5 q n/ sub 5 v 0 0.02 0.04 10-20% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 q n/ sub 5 v 0 0.02 0.04 30-40% =2.76 TeV NN sALICE Pb-Pb Particle species ± π ± K pp+ 0.5 1 1.5 2 2.5 0 0.02 0.04 5-10% 0.5 1 1.5 2 2.5 0 0.02 0.04 20-30% )c (GeV/ q n/ T p 0.5 1 1.5 2 2.5 0 0.02 0.04 40-50% Figure 10. The pT/nqdependence of vsub 4/nq(left figure) and vsub 5/nq(right figure) for π±, K±and p+p for Pb-Pb collisions in various centrality intervals at √sNN = 2.76 TeV. – 20 – JHEP09(2016)164 2 v 0 0.1 0.2 0.3 10-20% ALICE ± π ± K pp+ iEBE-VISHNU ± π ± K pp+ 0.5 1 1.5 2 2.5 2 v∆ 0.01− 0 0.01 0 0.1 0.2 0.3 =2.76 TeV NN sPb-Pb 20-30% 0.5 1 1.5 2 2.5 0.01 0 0.01 2 v 0 0.1 0.2 0.3 30-40% )c (GeV/ T p 0.5 1 1.5 2 2.5 2 v∆ 0.01− 0 0.01 0 0.1 0.2 0.3 40-50% )c (GeV/ T p 0.5 1 1.5 2 2.5 0.01 0 0.01 Figure 11. The pT-differential vsub 2for pions, kaons and protons measured with the Scalar Product method in Pb-Pb collisions at √sNN = 2.76 TeV compared to v2measured with iEBE-VISHNU. The upper panels present the comparison for 10–20% up to 40–50% centrality intervals. The thickness of the curves reflect the uncertainties of the hydrodynamical calculations. The differences between vsub 2from data and v2from iEBE-VISHNU are presented in the lower panels. 6.5 Comparison with models Measurements of vAA nat RHIC and LHC have been successfully described by hydrodynamical calculations. In particular in [23] it was shown that a hybrid model that couples the hydrodynamical expansion of the fireball to a hadronic cascade model describing the finalstate hadronic interactions is able to reproduce the basic features of the measurements at low values of pT. In parallel, various other models that incorporate a different description of the dynamical evolution of the system, such as AMPT, are also able to describe some of the main features of measurements of azimuthal anisotropy [50–52]. In this section, these two different theoretical approaches will be confronted with the experimental measurements. 6.5.1 Comparison with iEBE-VISHNU Figures 11,12 and 13 present the comparison between the ALICE measurements of vsub nand recent vnhydrodynamical calculations from [49]. These calculations are based on iEBEVISHNU, an event-by-event version of the VISHNU hybrid model [54] which couples 2+1 dimensional viscous hydrodynamics (VISH2+1) to a hadron cascade model (UrQMD) [55] and uses a set of fluctuating initial conditions generated with AMPT. The iEBE-VISHNU – 21 – JHEP09(2016)164 3 v 0 0.05 0.1 0.15 10-20% ALICE ± π ± K pp+ iEBE-VISHNU ± π ± K pp+ 0.5 1 1.5 2 2.5 3 v∆ 0.01− 0 0.01 0 0.05 0.1 0.15 =2.76 TeV NN sPb-Pb 20-30% 0.5 1 1.5 2 2.5 0.01 0 0.01 3 v 0 0.05 0.1 0.15 30-40% )c (GeV/ T p 0.5 1 1.5 2 2.5 3 v∆ 0.01− 0 0.01 0 0.05 0.1 0.15 40-50% )c (GeV/ T p 0.5 1 1.5 2 2.5 0.01 0 0.01 Figure 12. The pT-differential vsub 3for pions, kaons and protons measured with the Scalar Product method in Pb-Pb collisions at √sNN = 2.76 TeV compared to v3measured with iEBE-VISHNU. The upper panels present the comparison for 10–20% up to 40–50% centrality intervals. The thickness of the curves reflect the uncertainties of the hydrodynamical calculations. The differences between vsub 3from data and v3from iEBE-VISHNU are presented in the lower panels. model makes it possible to study the influence of the hadronic stage on the development of elliptic flow and higher harmonics for different particles. In this model, the initial time after which the hydrodynamic evolution begins is set to τ0= 0.4 fm/c and the transition between the macroscopic and microscopic approaches takes place at a temperature of T= 165 MeV. Finally, the value of the shear viscosity to entropy density ratio is chosen to be η/s = 0.08, corresponding to the conjectured lower limit discussed in the introduction. These input parameters were chosen to best fit the multiplicity and transverse momentum spectra of charged particles in most central Pb-Pb collisions as well as the pT-differential v2,v3, and v4for charged particles for various centrality intervals. These figures show that this hydrodynamical calculation can reproduce the observed mass ordering in the experimental data for pions, kaons and protons. In particular, it is seen that for the range 1 < pT<2 GeV/c in the 10–20% centrality interval the model overpredicts the pion vsub 2(pT) values by an average of 10%, however for more peripheral collisions the curve describes the data points relatively well. In addition, the model describes vsub 3and vsub 4for charged pions within 5%, i.e. better than vsub 2. Furthermore, it is seen that iEBE-VISHNU overpredicts the vsub 2(pT) values of K±(i.e. 10–15% deviations) – 22 – JHEP09(2016)164 4 v 0 0.05 0.1 0.15 10-20% ALICE ± π ± K pp+ iEBE-VISHNU ± π ± K pp+ 0.5 1 1.5 2 2.5 4 v∆ 0.01− 0 0.01 0 0.05 0.1 0.15 =2.76 TeV NN sPb-Pb 20-30% 0.5 1 1.5 2 2.5 0.01 0 0.01 4 v 0 0.05 0.1 0.15 30-40% )c (GeV/ T p 0.5 1 1.5 2 2.5 4 v∆ 0.01− 0 0.01 0 0.05 0.1 0.15 40-50% )c (GeV/ T p 0.5 1 1.5 2 2.5 0.01 0 0.01 Figure 13. The pT-differential vsub 4for pions, kaons and protons measured with the Scalar Product method in Pb-Pb collisions at √sNN = 2.76 TeV compared to v4measured with iEBE-VISHNU. The upper panels present the comparison for 10–20% up to 40–50% centrality intervals. The thickness of the curves reflect the uncertainties of the hydrodynamical calculations. The differences between vsub 4from data and v4from iEBE-VISHNU are presented in the lower panels. and does not describe p+p in more central collisions (i.e. by 10% with a different transverse momentum dependence compared to data), but in more peripheral collisions the agreement with the data points is better. Finally, the model describes the vsub 3(pT) and vsub 4(pT) values for K±and p+p with a reasonable accuracy (i.e. within 5%) in all centrality intervals up to pTaround 2 GeV/c. These observations are also illustrated in the lower plots of each panel in figures 11,12 and 13 that present the difference between the measured vsub nrelative to a fit to the hydrodynamical calculation. 6.5.2 Comparison with AMPT In addition to the hydrodynamical calculations discussed in the previous paragraphs, three different versions of AMPT [50–52] are studied in this article. The AMPT model can be run in two main configurations: the default and the string melting. In the default version, partons are recombined with the parent strings when they stop interacting. The resulting strings are later converted into hadrons using the Lund string fragmentation model [56,57]. In the string melting version, the initial strings are melted into partons whose interactions are described by a parton cascade model [58]. These partons are then combined into the – 23 – JHEP09(2016)164 0.5 1 1.5 2 2.5 2 v 0.1 0.2 0.3 string melting 0.5 1 1.5 2 2.5 3 v 0.05 0.1 0.15 )c (GeV/ T p 0.5 1 1.5 2 2.5 4 v 0 0.05 0.1 0.5 1 1.5 2 2.5 0.1 0.2 0.3 string melting without hadronic rescattering 0.5 1 1.5 2 2.5 0.05 0.1 0.15 AMPT ± π ± K pp+ )c (GeV/ T p 0.5 1 1.5 2 2.5 0 0.05 0.1 0.5 1 1.5 2 2.5 0.1 0.2 0.3 default 0.5 1 1.5 2 2.5 0.05 0.1 0.15 )c (GeV/ T p 0.5 1 1.5 2 2.5 0 0.05 0.1 Figure 14. The vAA 2(pT), vAA 3(pT) and vAA 4(pT) in 20–30% central Pb-Pb collisions at √sNN = 2.76 TeV, obtained using the string melting, with (left) and without (middle) hadronic rescattering, and the default (right) versions. final-state hadrons via a quark coalescence model. In both configurations a final-state hadronic rescattering is implemented which also includes resonance decays. The third version presented in this article is based on the string melting configuration, in which the hadronic rescattering phase is switched off to study its influence to the development of anisotropic flow. The input parameters used in all cases are: αs= 0.33, a partonic crosssection of 1.5 mb, while the Lund string fragmentation parameters were set to α= 0.5 and b= 0.9 GeV−2. Figure 14 presents the pT-differential v2(first row), v3(middle row) and v4(bottom row) for pions, kaons and protons for the 20–30% centrality interval. Each column presents the results of one of the three AMPT versions discussed above. The string melting AMPT version (left column) predicts a distinct mass ordering at low values of transverse momentum as well as a lower value of vnfor mesons compared to baryons in the intermediate pTregion for all harmonics, similar to what is observed in the experimental measurements. On the other hand, the version with string melting but without the hadronic rescattering – 24 – JHEP09(2016)164 0.5 1 1.5 ± π ) q n/ 2 sub v)/( q n/ 2 sub v( 0.5 1 1.5 0-1% 0.5 1 1.5 ± π ) q n/ 2 sub v)/( q n/ 2 sub v( 0.5 1 1.5 0-5% 0.5 1 1.5 ± π ) q n/ 2 sub v)/( q n/ 2 sub v( 0.5 1 1.5 10-20% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 ± π ) q n/ 2 sub v)/( q n/ 2 sub v( 0.5 1 1.5 30-40% 0.5 1 1.5 =2.76 TeV NN sALICE Pb-Pb Particle species ± K pp+ 0.5 1 1.5 0.5 1 1.5 5-10% 0.5 1 1.5 0.5 1 1.5 20-30% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 0.5 1 1.5 40-50% 0.5 1 1.5 ± π ) q n/ 3 sub v)/( q n/ 3 sub v( 0.5 1 1.5 0-1% 0.5 1 1.5 ± π ) q n/ 3 sub v)/( q n/ 3 sub v( 0.5 1 1.5 0-5% 0.5 1 1.5 ± π ) q n/ 3 sub v)/( q n/ 3 sub v( 0.5 1 1.5 10-20% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 ± π ) q n/ 3 sub v)/( q n/ 3 sub v( 0.5 1 1.5 30-40% 0.5 1 1.5 =2.76 TeV NN sALICE Pb-Pb Particle species ± K pp+ 0.5 1 1.5 0.5 1 1.5 5-10% 0.5 1 1.5 0.5 1 1.5 20-30% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 0.5 1 1.5 40-50% Figure 21. Left: the (mT−m0)/nqdependence of the double ratio of vsub 2/nqfor K±and p+p relative to a fit to vsub 2/nqof π±for Pb-Pb collisions in various centrality intervals at √sNN = 2.76 TeV. Right: the same for vsub 3/nq. 0.5 1 1.5 ± π ) q n/ 4 sub v)/( q n/ 4 sub v( 0.5 1 1.5 0-1% 0.5 1 1.5 ± π ) q n/ 4 sub v)/( q n/ 4 sub v( 0.5 1 1.5 0-5% 0.5 1 1.5 ± π ) q n/ 4 sub v)/( q n/ 4 sub v( 0.5 1 1.5 10-20% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 ± π ) q n/ 4 sub v)/( q n/ 4 sub v( 0.5 1 1.5 30-40% 0.5 1 1.5 =2.76 TeV NN sALICE Pb-Pb Particle species ± K pp+ 0.5 1 1.5 0.5 1 1.5 5-10% 0.5 1 1.5 0.5 1 1.5 20-30% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 0.5 1 1.5 40-50% 0.5 1 1.5 ± π ) q n/ 5 sub v)/( q n/ 5 sub v( 0.5 1 1.5 20-1% 0.5 1 1.5 ± π ) q n/ 5 sub v)/( q n/ 5 sub v( 0.5 1 1.5 20-5% 0.5 1 1.5 ± π ) q n/ 5 sub v)/( q n/ 5 sub v( 0.5 1 1.5 210-20% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 ± π ) q n/ 5 sub v)/( q n/ 5 sub v( 0.5 1 1.5 230-40% 0.5 1 1.5 =2.76 TeV NN sALICE Pb-Pb Particle species ± K pp+ 0.5 1 1.5 0.5 1 1.5 25-10% 0.5 1 1.5 0.5 1 1.5 220-30% ) 2 c (GeV/ q n)/ 0 mT m( 0.5 1 1.5 0.5 1 1.5 240-50% Figure 22. 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Poghosyan87 , B. Polichtchouk113 , N. Poljak131 , W. Poonsawat116 , A. Pop80 , H. Poppenborg56 , S. Porteboeuf-Houssais72 , J. Porter76 , J. Pospisil86 , S.K. Prasad4, R. Preghenella106 ,36 , F. Prino112 , C.A. Pruneau137 , I. Pshenichnov58 , M. Puccio26 , G. Puddu24 , P. Pujahari137 , V. Punin101 , J. Putschke137 , H. Qvigstad22 , A. Rachevski111 , S. Raha4, S. Rajput93 , J. Rak125 , A. Rakotozafindrabe15 , L. Ramello31 , F. Rami57 , R. Raniwala94 , S. Raniwala94 , S.S. R¨as¨anen47 , B.T. Rascanu55 , D. Rathee90 , I. Ravasenga26 , K.F. Read127 ,87 , K. Redlich79 , R.J. Reed137 , A. Rehman18 , P. Reichelt55 , F. Reidt36 ,96 , X. Ren7, R. Renfordt55 , A.R. Reolon74 , A. Reshetin58 , K. Reygers96 , V. Riabov88 , R.A. Ricci75 , T. Richert34 , M. Richter22 , P. Riedler36 , W. Riegler36 , F. Riggi28 , C. Ristea64 , M. Rodr´ıguez Cahuantzi2, A. Rodriguez Manso84 , K. Røed22 , E. Rogochaya68 , D. Rohr43 , D. R¨ohrich18 , F. Ronchetti36 ,74 , L. Ronflette115 , P. Rosnet72 , A. Rossi29 , F. Roukoutakis91 , A. Roy50 , C. Roy57 , P. Roy102 , A.J. Rubio Montero10 , R. Rui25 , R. Russo26 , E. Ryabinkin82 , Y. Ryabov88 , A. Rybicki119 , S. Saarinen47 , S. Sadhu135 , S. Sadovsky113 , K. ˇ Safaˇr´ık36 , B. Sahlmuller55 , P. Sahoo50 , R. Sahoo50 , S. Sahoo63 , P.K. Sahu63 , J. Saini135 , S. Sakai74 , M.A. Saleh137 , J. Salzwedel20 , S. Sambyal93 , V. Samsonov88 ,77 , L. ˇ S´andor61 , A. Sandoval66 , M. Sano130 , D. Sarkar135 , N. Sarkar135 , P. Sarma45 , E. Scapparone106 , F. Scarlassara29 , C. Schiaua80 , R. Schicker96 , C. Schmidt99 , H.R. Schmidt35 , M. Schmidt35 , S. Schuchmann55 ,96 , J. Schukraft36 , Y. Schutz36 ,115 , K. Schwarz99 , K. Schweda99 , G. Scioli27 , E. Scomparin112 , R. Scott127 , M. ˇ Sefˇc´ık41 , J.E. Seger89 , Y. Sekiguchi129 , D. Sekihata48 , I. Selyuzhenkov99 , K. Senosi67 , S. Senyukov3,36 , E. Serradilla10 ,66 , A. Sevcenco64 , – 38 – JHEP09(2016)164 A. Shabanov58 , A. Shabetai115 , O. Shadura3, R. Shahoyan36 , A. Shangaraev113 , A. Sharma93 , M. Sharma93 , M. Sharma93 , N. Sharma127 , A.I. Sheikh135 , K. Shigaki48 , Q. Shou7, K. Shtejer9,26 , Y. Sibiriak82 , S. Siddhanta107 , K.M. Sielewicz36 , T. Siemiarczuk79 , D. Silvermyr34 , C. Silvestre73 , G. Simatovic131 , G. Simonetti36 , R. Singaraju135 , R. Singh81 , V. Singhal135 , T. Sinha102 , B. Sitar39 , M. Sitta31 , T.B. Skaali22 , M. Slupecki125 , N. Smirnov139 , R.J.M. Snellings59 , T.W. Snellman125 , J. Song98 , M. Song140 , Z. Song7, F. Soramel29 , S. Sorensen127 , F. Sozzi99 , E. Spiriti74 , I. Sputowska119 , M. Spyropoulou-Stassinaki91 , J. Stachel96 , I. Stan64 , P. Stankus87 , E. Stenlund34 , G. Steyn67 , J.H. Stiller96 , D. Stocco115 , P. Strmen39 , A.A.P. Suaide122 , T. Sugitate48 , C. Suire53 , M. Suleymanov16 , M. Suljic25 ,i, R. Sultanov60 , M. ˇ Sumbera86 , S. Sumowidagdo51 , S. Swain63 , A. Szabo39 , I. Szarka39 , A. Szczepankiewicz136 , M. Szymanski136 , U. Tabassam16 , J. Takahashi123 , G.J. Tambave18 , N. Tanaka130 , M. Tarhini53 , M. Tariq19 , M.G. Tarzila80 , A. Tauro36 , G. Tejeda Mu˜noz2, A. Telesca36 , K. Terasaki129 , C. Terrevoli29 , B. Teyssier132 , J. Th¨ader76 , D. Thakur50 , D. Thomas120 , R. Tieulent132 , A. Tikhonov58 , A.R. Timmins124 , A. Toia55 , S. Trogolo26 , G. Trombetta33 , V. Trubnikov3, W.H. Trzaska125 , T. Tsuji129 , A. Tumkin101 , R. Turrisi109 , T.S. Tveter22 , K. Ullaland18 , A. Uras132 , G.L. Usai24 , A. Utrobicic131 , M. Vala61 , L. Valencia Palomo72 , J. Van Der Maarel59 , J.W. Van Hoorne36 ,114 , M. van Leeuwen59 , T. Vanat86 , P. Vande Vyvre36 , D. Varga138 , A. Vargas2, M. Vargyas125 , R. Varma49 , M. Vasileiou91 , A. Vasiliev82 , A. Vauthier73 , O. V´azquez Doce95 ,37 , V. Vechernin134 , A.M. Veen59 , A. Velure18 , E. Vercellin26 , S. Vergara Lim´on2, R. Vernet8, L. Vickovic118 , J. Viinikainen125 , Z. Vilakazi128 , O. Villalobos Baillie103 , A. Villatoro Tello2, A. Vinogradov82 , L. Vinogradov134 , T. Virgili30 , V. Vislavicius34 , Y.P. Viyogi135 , A. Vodopyanov68 , M.A. V¨olkl96 , K. 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Zimmermann56 ,36 , G. Zinovjev3, M. Zyzak43 iDeceased ii Also at: Georgia State University, Atlanta, Georgia, United States iii Also at: Also at Department of Applied Physics, Aligarh Muslim University, Aligarh, India iv Also at: M.V. Lomonosov Moscow State University, D.V. Skobeltsyn Institute of Nuclear, Physics, Moscow, Russia 1A.I. Alikhanyan National Science Laboratory (Yerevan Physics Institute) Foundation, Yerevan, Armenia 2Benem´erita Universidad Aut´onoma de Puebla, Puebla, Mexico 3Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine 4Bose Institute, Department of Physics and Centre for Astroparticle Physics and Space Science (CAPSS), Kolkata, India – 39 – JHEP09(2016)164 5Budker Institute for Nuclear Physics, Novosibirsk, Russia 6California Polytechnic State University, San Luis Obispo, California, United States 7Central China Normal University, Wuhan, China 8Centre de Calcul de l’IN2P3, Villeurbanne, France 9Centro de Aplicaciones Tecnol´ogicas y Desarrollo Nuclear (CEADEN), Havana, Cuba 10 Centro de Investigaciones Energ´eticas Medioambientales y Tecnol´ogicas (CIEMAT), Madrid, Spain 11 Centro de Investigaci´on y de Estudios Avanzados (CINVESTAV), Mexico City and M´erida, Mexico 12 Centro Fermi - Museo Storico della Fisica e Centro Studi e Ricerche “Enrico Fermi”, Rome, Italy 13 Chicago State University, Chicago, Illinois, USA 14 China Institute of Atomic Energy, Beijing, China 15 Commissariat `a l’Energie Atomique, IRFU, Saclay, France 16 COMSATS Institute of Information Technology (CIIT), Islamabad, Pakistan 17 Departamento de F´ısica de Part´ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain 18 Department of Physics and Technology, University of Bergen, Bergen, Norway 19 Department of Physics, Aligarh Muslim University, Aligarh, India 20 Department of Physics, Ohio State University, Columbus, Ohio, United States 21 Department of Physics, Sejong University, Seoul, South Korea 22 Department of Physics, University of Oslo, Oslo, Norway 23 Dipartimento di Fisica dell’Universit`a ’La Sapienza’ and Sezione INFN Rome, Italy 24 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Cagliari, Italy 25 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Trieste, Italy 26 Dipartimento di Fisica dell’Universit`a and Sezione INFN, Turin, Italy 27 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Bologna, Italy 28 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Catania, Italy 29 Dipartimento di Fisica e Astronomia dell’Universit`a and Sezione INFN, Padova, Italy 30 Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit`a and Gruppo Collegato INFN, Salerno, Italy 31 Dipartimento di Scienze e Innovazione Tecnologica dell’Universit`a del Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy 32 Dipartimento DISAT del Politecnico and Sezione INFN, Turin, Italy 33 Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy 34 Division of Experimental High Energy Physics, University of Lund, Lund, Sweden 35 Eberhard Karls Universit¨at T¨ubingen, T¨ubingen, Germany 36 European Organization for Nuclear Research (CERN), Geneva, Switzerland 37 Excellence Cluster Universe, Technische Universit¨at M¨unchen, Munich, Germany 38 Faculty of Engineering, Bergen University College, Bergen, Norway 39 Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia 40 Faculty of Nuclear Sciences and Physical Engineering, Czech Technical University in Prague, Prague, Czech Republic 41 Faculty of Science, P.J. ˇ Saf´arik University, Koˇsice, Slovakia 42 Faculty of Technology, Buskerud and Vestfold University College, Vestfold, Norway 43 Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨at Frankfurt, Frankfurt, Germany 44 Gangneung-Wonju National University, Gangneung, South Korea 45 Gauhati University, Department of Physics, Guwahati, India 46 Helmholtz-Institut f¨ur Strahlenund Kernphysik, Rheinische Friedrich-Wilhelms-Universit¨at Bonn, Bonn, Germany 47 Helsinki Institute of Physics (HIP), Helsinki, Finland 48 Hiroshima University, Hiroshima, Japan 49 Indian Institute of Technology Bombay (IIT), Mumbai, India 50 Indian Institute of Technology Indore, Indore (IITI), India 51 Indonesian Institute of Sciences, Jakarta, Indonesia – 40 –