Anisotropic flow and other collective phenomena measured in Pb-Pb collisions with ALICE at the LHC
11 Anisotropic flow and other collective phenomena measured inPb-Pb collisions with ALICE at the LHC
Ilya
Selyuzhenkov for the ALICE Collaboration
Research Division and ExtreMe Matter Institute EMMI,GSI Helmholtzzentrum f¨ur Schwerionenforschung, Darmstadt, Germany
Recent results of the anisotropic flow measurements by the ALICE Collaboration atthe LHC are reviewed. Directed, elliptic, triangular, and quadrangular flow are presenteddifferentially vs. transverse momentum, pseudo-rapidity, and the collision centrality forcharged and identified particles. Experimental probes of local parity violation using thecharge dependent azimuthal correlations with respect to the reaction plane are also discussed. §
1. Introduction
An azimuthal anisotropic flow describes a collectivity among particles producedin heavy-ion collision, and it is recognized as one of the key observable which providesinformation on the early time evolution of the nuclei interaction. This ISMD2011Conference proceedings highlight recent results by the ALICE Collaboration from theanisotropic flow measurements for Pb-Pb collisions at √ s NN = 2.76 GeV. Currentstatus of probes of parity symmetry violation in strong interaction using the chargedependent azimuthal correlations with respect to the reaction plane is also discussed. §
2. Anisotropic flow, fluctuations, and non-flow correlations
Anisotropic transverse flow is usually quantified by the coefficients (harmonics)in the Fourier decomposition of the azimuthal distribution of particles with respectto the reaction plane. The collision reaction plane, which is defined by the impactparameter and the colliding nuclei direction, is not known experimentally and theanisotropic flow coefficients can be only extracted from azimuthal correlations be-tween produced particles (for review of the anisotropic flow measurement techniquessee ). The main challenge in the anisotropic flow measurement is to disentanglecontribution from correlations not related to the reaction plane (so called non-flowcorrelations), and to understand the impact on the measured flow from the event-by-event fluctuations (e.g. due to fluctuating energy density in the overlap zone oftwo nuclei).Figure 1(a) shows a systematic study of non-flow and flow fluctuations for theelliptic flow, v , measured for Pb-Pb collisions at √ s NN = 2.76 GeV. The magnitudeof non-flow effects is driven by the difference between v estimated from the two-particle azimuthal correlations without ( v { , | ∆η | > } ) and with ( v { , | ∆η | > } )pseudo-rapidity separation between correlated particles which greatly suppress non-flow effects from short-range correlations. Flow fluctuations can be estimated fromthe difference between the results from two-particle correlations with a large rapiditygap and those from multi- (4, 6, and 8) particle cumulants (for an estimate of the a r X i v : . [ nu c l - e x ] N ov Ilya Selyuzhenkov centrality percentile v = 2.76 TeV NN sALICE Preliminary, Pb Pb events at (charged hadrons) v > 0) η∆ ({2} v > 1) η∆ ({2} v {4} v {6} v {8} v (GeV/c) t p v NN sALICE preliminary, Pb Pb events at centrality 10% 20%|>1} η∆ {SP, | , v ± π |>1} η∆ {SP, | , v ± K |>1} η∆ {SP, | , vp (CGC initial conditions)/s=0.2) η (hydro LHChydro+UrQMD LHC (a) (b) Fig. 1. Elliptic flow, v , measured for Pb-Pb collisions at √ s NN = 2.76 TeV. (a) v of chargedparticles vs. centrality, (b) v vs. transverse momentum for pions, kaons, and anti-protons.Figure (a) taken from and figure (b) from . elliptic flow fluctuations under the assumption of the small or Gaussian fluctuationssee ). The results in Fig. 1(a) show that both flow fluctuations and non-flow (mainlyfor the peripheral collisions) are significant and have to be seriously taken into ac-count when comparing measured anisotropic flow with theoretical calculations. §
3. Elliptic flow of identified particles
Since the success of the ideal hydrodynamic description of the elliptic flow, v ,for the central Au-Au collisions at RHIC , the hydrodynamics is considered as themost appropriate theory to describe a thermalized phase in the time evolution ofthe system created in a heavy-ion collision. An important test of the hydrodynamicdescription at the LHC is the interplay between radial (azimuthally symmetric radialexpansion) and anisotropic flow which result in the mass splitting of the elliptic flowat small transverse momenta. Figure 1(b) shows the elliptic flow of pions, kaons,and anti-protons vs. particle transverse momenta, p t , measured with the scalarproduct (SP) method. The mass dependence of v at low transverse momenta, p t < . with a color glass condensate initial condition (solid lines in Fig. 1(b)). Agreementwith data, especially for protons, is improved when adding a hadronic cascade phaseinto the model calculations (dashed lines in Fig. 1(b)). Figure 2(a) shows elliptic flowof pions, kaons, and anti-protons scaled with the number of constituent quarks, n q ( n q = 2 for mesons, and n q = 3 for baryons), vs. transverse kinetic energy per quark,( m t − m ) /n q . The observed approximate scaling of v with the number of quarksin the range of p t ∼ − m t ∼ . − . / c ) reflects collectivity at thequark level and suggest that the system evolved through the phase of deconfinedquarks and gluons. low and other collective phenomena with ALICE ) (GeV/c q )/n -m t (m q / n v = 2.76 TeV NN sALICE preliminary, Pb-Pb events at centrality 10%-20%|>1} η∆ {SP, | , v ± π |>1} η∆ {SP, | , v ± K |>1} η∆ {SP, | , vp ) (GeV/c q )/n -m t (m q / n v -0.0100.010.020.030.040.050.06 = 2.76 TeV NN sALICE preliminary, Pb-Pb events at centrality 10%-20% ± π {2} v ± K{2} v p {2} v (a) (b) Fig. 2. (a) Elliptic, v , and (b) triangular, v , flow measured with the scalar product (SP) methodfor Pb-Pb collisions at √ s NN = 2.76 TeV. Elliptic and triangular flow are scaled with theconstituent number of quarks and plotted vs. transverse kinetic energy per quark. Figurestaken from . §
4. Triangular and higher harmonic flow
Recent progress in understanding the connection between the anisotropic flowand the fluctuations of the energy density in the initial state of the heavy-ion collisionshowed that not only the dominant elliptic flow component is important, but thatother harmonics such as triangular flow are crucial for the realistic description ofthe system created during the collision (see and references therein). Figure 3(a) centrality percentile n v ALICE > 1} hD {2, v > 1} hD {2, v > 1} hD {2, v {4} v RP Y v Y v · Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 034813 (2010) /s=0.08 h Glauber v /s=0.16 h CGC v (a) (b) Fig. 3. (a) Elliptic, triangular, and quadrangular flow vs. collision centrality measured for Pb-Pbcollisions at √ s NN = 2.76 TeV. (b) Two-particle azimuthal correlations measured with large( | η | >
1) rapidity separation between particles and their decomposition into anisotropic flowharmonics. Figure (a) taken from and figure (b) from . shows elliptic, triangular, and quadrangular flow vs. collision centrality measuredwith two- and four-particle correlations for Pb-Pb collisions at √ s NN = 2.76 TeV.Measured triangular flow, v , behaves as it is expected for collective correlations fromthe fluctuations of the initial geometry, i.e. i) weak centrality dependence followscalculations with fluctuating initial condition (solid blue squares vs. dotted black Ilya Selyuzhenkov line), ii) “proper” ratio of v { } /v { } ≈ , and iii) no correlation of v with respect to the true reaction plane ( v measured with the reaction plane estimated from deflection of neutron spectators isconsistent with zero, see green points in Fig. 3(a)), iv) no correlation between v and the azimuthal modulations in the second flow harmonic, v (black diamonds inFig. 3(a)). Another evidence for the collective origin of the triangular flow is thesimilar mass splitting and the number of quark scaling to that of elliptic flow which isdemonstrated in Fig 2(b). Note that in contrast to the v results in Fig. 2(a), thereis no pseudo-rapidity separation between correlated particles in v measurementswhich may results in the additional bias at small ( m t − m ) /n q values.It is remarkable that including higher-order flow harmonics allows to reproducethe “ridge” and “Mach-cone” features of the two-particle azimuthal correlations atlow transverse momenta (see Fig. 3(b)), which were originally interpreted as resultsof the propagation of the hard probe (e.g. jet) through the dense medium. §
5. Directed flow
Directed flow, v , is sensitive to the earliest, pre-equilibrium, times in the evo-lution of the system (see and references therein). Figure 4(a) shows v of charged η pseudorapidity,
4 2 0 2 4 d i r e c t ed f l o w , v × Centrality 0 80% stat. & syst. errors
TPC VZERO η + B η ) = A η Combined fit ( = 2.76 TeV NN sALICE Preliminary Pb Pb at beam y η
8 6 4 2 0 d i r e c t ed f l o w , v = 2.76 TeV NN sALICE Pb Pb at = 200 GeV NN sSTAR Au Au at = 62 GeV NN sSTAR Au Au at = 200 GeV NN sSTAR Cu Cu at = 62 GeV NN sSTAR Cu Cu at = 2.76 TeV NN sALICE Pb Pb at = 200 GeV NN sSTAR Au Au at = 62 GeV NN sSTAR Au Au at = 200 GeV NN sSTAR Cu Cu at = 62 GeV NN sSTAR Cu Cu at Preliminary stat. & syst. errors (a) (b) Fig. 4. Directed flow, v , for Pb-Pb collisions at √ s NN = 2.76 TeV. (a) v over large rapidity range, | η | < .
1. (b) longitudinal scaling of v . Figures taken from . particles measured in a wide rapidity range with the reaction plane estimated fromthe deflection of the spectator neutrons at beam rapidity. The absolute sign of di-rected flow is fixed in the measurement by the same convention as used at RHIC,i.e. spectators with η > v . The measured negative slope of v as a function of pseudo-rapidity is opposite to the predictions for LHC energiesfrom the quark-gluon string model with parton rearrangement and fluid dynami-cal calculations which suggest a much stronger signal with a positive slope of v .Figure 4(b) shows v measured as a function of beam rapidity which is consistentwith the longitudinal scaling previously observed at RHIC energies. low and other collective phenomena with ALICE §
6. Probes of local parity violation in strong interaction
The extreme magnetic field created during a non-central relativistic heavy-ioncollision may spontaneously excite instantons and sphalerons from the QCD vac-uum which violates parity symmetry of the strong interactions. It is predicted byKharzeev et al. that this may result in the experimentally observable separation ofcharges along the magnetic field. Since the magnetic field is perpendicular to the col-lision reaction plane, Voloshin proposed to use the anisotropic flow measurementtechnique to experimentally probe the effects of charge separation. Figure 5(a) shows centrality, % 〉 ) R P Ψ β φ + α φ c o s ( 〈 × = 2.76 TeV NN s ALICE Pb Pb @ = 0.2 TeV NN s STAR Au Au @ same opp. Preliminary centrality, % 〉 ) β φ α φ c o s ( 〈 × same opp. = 2.76 TeV NN s ALICE Pb Pb @ = 0.2 TeV NN s STAR Au Au @ Preliminary (a) (b) Fig. 5. Charged dependent azimuthal correlations vs. centrality measured for Pb-Pb collisionsat √ s NN = 2.76 TeV and Au-Au collisions at √ s NN = 0.2 TeV: (a) two-particle correlationswith respect to the reaction plane, (b) 1st harmonic two-particle correlations. Figures adaptedfrom . the experimental results for the charge-dependent two-particle correlation with re-spect to the reaction plane: (cid:104) cos( φ α + φ β − Ψ RP ) (cid:105) , where φ α,β is the azimuthal angleand α, β charge of the particle, and Ψ RP is the reaction plane angle. Clear charge sep-aration is observed at both RHIC and LHC energies with a very similar magnitudeand centrality dependence of the correlations. The (cid:104) cos( φ α + φ β − Ψ RP ) (cid:105) observablehas direct sensitivity to the event-by-event charge fluctuations, but it is parity evenand thus is sensitive to effect unrelated to the symmetry violation. The presenceof parity even background correlations which contributes to the measured chargeseparation at RHIC and LHC significantly complicates the interpretation of thedata. Among possibly large contributions from the parity even backgrounds are flowfluctuations in the first flow harmonic and effects of local charge conservation .Figure 5(b) presents the 1st harmonic two-particle correlations, (cid:104) cos( φ α − φ β ) (cid:105) , whichin contrast to the (cid:104) cos( φ α + φ β − Ψ RP ) (cid:105) show opposite sign at LHC than at RHICfor the same charge correlations. Results for the (cid:104) cos( φ α − φ β ) (cid:105) correlator are domi-nated by the parity conserving background sources and this may provide additionalinsights on the origin of the measured charge separation. Currently, large theoreticaluncertainties in the estimate of background correlations as well as lack of quanti-tative predictions from the models which incorporate parity symmetry violation inQCD make the data interpretation difficult and further theoretical developments in Ilya Selyuzhenkov this direction are extremely important. §
7. Summary and outlook
The anisotropic flow harmonics up to the fifth order have been measured forPb-Pb collisions at √ s NN = 2.76 GeV by the ALICE Collaboration at the LHC. Al-together, directed, elliptic, triangular, and quadrangular flow measurements providestrong constraints on the properties of the system created during the heavy-ion colli-sion such as viscosity, initial conditions, and the equation of state. Charge separationof particles with respect to the collision reaction plane, which was first observed atRHIC energies, is now measured for Pb-Pb collisions at √ s NN = 2.76 GeV by theALICE Collaboration at the LHC. The charge-dependent two-particle azimuthal cor-relations with respect to the reaction plane are very similar to that at RHIC energies,while the background dominated 1st harmonic two-particle azimuthal correlationsshow a different sign at LHC than at RHIC for the same charge correlations. Thisprovides strong experimental constraints on the possible mechanism of the measuredcharge separation. Acknowledgements
This work was supported by the Helmholtz Alliance Program of the HelmholtzAssociation, contract HA216/EMMI “Extremes of Density and Temperature: Cos-mic Matter in the Laboratory”.
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