Review of collective flow at RHIC and LHC

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1 Review of collective flow at RHIC and LHC Jaap Onderwaater 29 November 2012 J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

2 Heavy ion collision stages Outline Heavy ion collisions and flow Experimental methods to determine flow Flow results from RHIC and LHC Fluctuations and higher harmonics J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Heavy ion collision stages Three stages in beam side view Space/time evolution of HIC Transverse expansion t 1fm/c (3 10 24 s) 1fm/c 10fm/c t

3 Heavy ion collision stages Three stages in beam side view Space/time evolution of HIC Transverse expansion t 1fm/c ( s) 1fm/c 10fm/c t 10fm/c t > 10fm/c QGP is formed Expansion (hydrodynamics) Hadronization Freeze-out J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

4 Heavy ion collisions - impact parameter and nucleon scaling Heavy ions approach each other with center-to-center displacement: Impact parameter - b J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

5 Heavy ion collisions - impact parameter and nucleon scaling Heavy ions approach each other with center-to-center displacement: Impact parameter - b Beam line view: J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

6 Heavy ion collisions - impact parameter and nucleon scaling Heavy ions approach each other with center-to-center displacement: Impact parameter - b Beam line view: Spatial eccentricity: ɛ = y 2 x 2 y 2 + x 2 J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

7 Time evolution of spatial and momentum anisotropy Spatial asymmetry transforms into momentum asymmetry. ɛ = y 2 x 2 y 2 + x 2 ɛ = T xx T yy T xx + T yy Spatial momentum drops very fast. Momentum asymmetry develops very early. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

8 Quantifying the final momentum aniostropy Elleptic flow (v 2 ) and directed flow (v 1 ) result in momentum profile which can be expanded in a Fourier series. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

9 Quantifying the final momentum aniostropy Elleptic flow (v 2 ) and directed flow (v 1 ) result in momentum profile which can be expanded in a Fourier series. cos(2φ) cos(φ) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

10 Quantifying the final momentum aniostropy Elleptic flow (v 2 ) and directed flow (v 1 ) result in momentum profile which can be expanded in a Fourier series. cos(2φ) cos(φ) E d 3 N d 3 p = 1 2π d 2 N p T dp T dy (1 + 2v n cos(nφ)), n=1 v n = cos(nφ i ). J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

11 Centrality dependence of flow Peripheral collisions have more spatial asymmetry and exhibit stronger elleptic flow. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

12 Centrality dependence of flow Peripheral collisions have more spatial asymmetry and exhibit stronger elleptic flow. Not so fast... J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

13 Measuring the particle azimuthal distributions Angular distribution of the impact parameter with respect to the laboratory frame fluctuates event by event. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

14 Measuring the particle azimuthal distributions Angular distribution of the impact parameter with respect to the laboratory frame fluctuates event by event. Average of azimuthal distributions is zero in lab frame over many events. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

15 Ultra-relativistic heavy ion colliders J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

9 Calorimetry and rare probes: neutral particles, photons, jets, heavy flavor, spectator

16 A Heavy Ion Experiment Full azumuthal coverage Rapidity coverage η < 5. Features of ALICE: Charge particle tracking and identification: p T GeV/c for η < 0.9 Calorimetry and rare probes: neutral particles, photons, jets, heavy flavor, spectator neutrons and protons at beam rapidity. 0.5 T magnetic field J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

17 Particle identification Particle tracking and identification with ALICE. Lepton and hadron identification from GeV/c Time resolution of 80ps. Seperation of kaons, pions and protons up to few GeV/c. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

18 Determining the impact parameter Magnitude of impact parameter is inferred from measured produced particle multiplicities or number of spectators. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

19 Azimuthal distribution wrt reaction plane Describe distributions with respect to the event symmetry plane. Plane spanned by impact parameter and beam direction. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

20 Azimuthal distribution wrt reaction plane Describe distributions with respect to the event symmetry plane. Plane spanned by impact parameter and beam direction. Realign the events wrt to symmetry plane: J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Now the Fourier series has to be written as:

21 Azimuthal distribution wrt reaction plane Describe distributions with respect to the event symmetry plane. Plane spanned by impact parameter and beam direction. Realign the events wrt to symmetry plane: Now the Fourier series has to be written as: dn d(φ i Ψ n ) n=1 v n cos(n(φ i Ψ n )) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

22 Azimuthal distribution wrt reaction plane dn d(φ i Ψ n ) n=1 v n cos(n(φ i Ψ n )) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

23 Azimuthal distribution wrt reaction plane dn d(φ i Ψ n ) v n cos(n(φ i Ψ n )) n=1 Fourier coefficient v n is given by: v n = cos(n(φ i Ψ n )) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

24 Azimuthal distribution wrt reaction plane dn d(φ i Ψ n ) n=1 Fourier coefficient v n is given by: v n = cos(n(φ i Ψ n )) v n cos(n(φ i Ψ n )) But the collision symmetry plane orientation is not known experimentally! J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

25 Analysis method with reaction plane Reaction plane can not directly be measured in experiment, but is determined with particle azimuthal distributions. Q-vector: Q n M i=1 e inφ i M e inφ i = Q n e inψ Qn = Qn,x + iq n,y i=1 Q n,x = Q n cos(nψ Qn ) Q n,x = Q n sin(nψ Qn ) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

26 Analysis method with reaction plane Ψ n EP = 1 2 arctan 2(Q n,y, Q n,x ) The observed v obs n is retrieved with the event average: v obs n = cos(n[φ Ψ EP ]) Event plane resolution due to finite multiplicity: R = cos(n[ψ EP Ψ n ]) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

27 Event plane method Event plane resolution relates to the flow coefficients (sin terms are 0 so we can write in complex numbers): v n = e (in[φ Ψn]), = e (in[φ Ψ EP])+(in[Ψ EP Ψ n]), = e(in[φ Ψ EP ]) = v e ( in[ψ EP Ψn]) n obs R J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

28 Event plane method Event plane resolution relates to the flow coefficients (sin terms are 0 so we can write in complex numbers): v n = e (in[φ Ψn]), = e (in[φ Ψ EP])+(in[Ψ EP Ψ n]), = e(in[φ Ψ EP ]) = v e ( in[ψ EP Ψn]) n obs R This approach already contains complicated correlations between multiple particles. A more simple approach is possible. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Two particle correlations An estimate of flow can be given with particles correlations : e i2(φ 1 φ 2 ) = e i2(φ 1 Ψ RP (φ 2 Ψ RP )), = e i2(φ 1 Ψ RP ) e i2(φ 2 Ψ RP ) + δ 2, = v 2 2 + δ

29 Two particle correlations An estimate of flow can be given with particles correlations : e i2(φ 1 φ 2 ) = e i2(φ 1 Ψ RP (φ 2 Ψ RP )), = e i2(φ 1 Ψ RP ) e i2(φ 2 Ψ RP ) + δ 2, = v δ 2 δ 2 : Correlations independent of Reaction Plane (non-flow). v 2 > 0 v 2 {2} > 0 v 2 = 0 v 2 {2} = 0 v 2 = 0 v 2 {2} > 0 J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

30 Suppressing non-flow with η-gap In order to reduce contribution from non-flow (e.g. decays and jets), an η-gap can be applied. Correlate particles with η 0. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

31 Suppressing non-flow with multi-particle correlations Contribution from non-flow can be suppressed using multi-particle correlations. c n {2} e in(φ 1 φ 2 ) e in(φ 1 φ 2 ) e inφ 1 e inφ 2, = e in(φ 1 φ 2 ) = v 2 n + δ n, J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

32 Suppressing non-flow with multi-particle correlations Contribution from non-flow can be suppressed using multi-particle correlations. c n {2} e in(φ 1 φ 2 ) e in(φ 1 φ 2 ) e inφ 1 e inφ 2, = e in(φ 1 φ 2 ) = v 2 n + δ n, c n {4} e in(φ 1+φ 2 φ 3 φ 4 ) e in(φ 1+φ 2 φ 3 φ 4 ) 2 e in(φ 1 φ 3 ) 2, = v 4 n + δ 2n v 2 n δ n + 2δ 2 n 2(v 2 n + δ n ) 2, = v 4 n J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

33 Suppressing non-flow with multi-particle correlations Contribution from non-flow can be suppressed using multi-particle correlations. c n {2} e in(φ 1 φ 2 ) e in(φ 1 φ 2 ) e inφ 1 e inφ 2, = e in(φ 1 φ 2 ) = v 2 n + δ n, c n {4} e in(φ 1+φ 2 φ 3 φ 4 ) e in(φ 1+φ 2 φ 3 φ 4 ) 2 e in(φ 1 φ 3 ) 2, = v 4 n + δ 2n v 2 n δ n + 2δ 2 n 2(v 2 n + δ n ) 2, = v 4 n From combinatorics, non-flow drops with δ 2 1/M, with M the particle multiplicity. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

34 Suppressing non-flow with multi-particle correlations Contribution from non-flow can be suppressed using multi-particle correlations. c n {2} e in(φ 1 φ 2 ) e in(φ 1 φ 2 ) e inφ 1 e inφ 2, = e in(φ 1 φ 2 ) = v 2 n + δ n, c n {4} e in(φ 1+φ 2 φ 3 φ 4 ) e in(φ 1+φ 2 φ 3 φ 4 ) 2 e in(φ 1 φ 3 ) 2, = v 4 n + δ 2n v 2 n δ n + 2δ 2 n 2(v 2 n + δ n ) 2, = v 4 n From combinatorics, non-flow drops with δ 2 1/M, with M the particle multiplicity. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

35 Energy dependence of elleptic flow Elleptic flow vs. centrality Over 4 decades of data taking spanning GSI, AGS, SPS, RHIC and LHC experiments. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

36 Energy dependence of elleptic flow Elleptic flow vs. centrality Over 4 decades of data taking spanning GSI, AGS, SPS, RHIC and LHC experiments. 30% increase of v 2 from RHIC: stronger collectivity at LHC. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

charged particles Agreement of v 2 (p T ) covers almost two orders of

37 Increase of flow due to stronger radial flow Increase of v 2 because of increase in p T -differential flow higher average transverse momentum of charged particles Agreement of v 2 (p T ) covers almost two orders of magnitude. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

38 Pseudorapidity dependence of flow v 2 vs pseudorapidity Dependence on dn ch /dη. Lower particle multiplicity results in less flow. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

respect to the beam rapidity. Extrapolation predicts an increase of v 2 of 50%.

39 Flow with respect to beam rapidity Longitudinal scaling. Integrated elleptic flow depends linearly on the pseudorapidity η, measured with respect to the beam rapidity. Extrapolation predicts an increase of v 2 of 50%. Centrality dependence extrapolation agrees with ALICE measurement. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

40 Flow with respect to beam rapidity: resent results Longitudinal scaling. Integrated elleptic flow depends linearly on the pseudorapidity η, measured with respect to the beam rapidity. elleptic flow directed flow Towards the beam rapidity the directed and elliptic flow show universal trend. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Particle type dependence of v 2 Differential flow shows

φ-meson v 2 : At low p T follows mass dependence For

41 Particle type dependence of v 2 Differential flow shows mass dependence. Mass dependence reproduced by viscous hydrodynamics sensitive to initial conditions low viscosity of matter φ-meson v 2 : At low p T follows mass dependence For higher p T mesons scales with other J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

42 Constituent quark scaling at RHIC Identified particles exhibit scaling with the number of constituent quarks. d 3 n M d 3 p M [ d 3 n q d 3 p q (p q p M /2)] 2 d 3 n B d 3 p B [ d 3 n q d 3 p q (p q p B /3)] 3 v 2 (p T ) nv 2 (p T /n) Indication that the system is in a deconfined stage. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

d 3 n M d 3 p M [ d 3 n q d 3 p q (p q p M /2)] 2 d 3 n B d 3 p B [ d 3 n q d 3 p q (p q p B /3)] 3 v 2

43 Constituent quark scaling at RHIC Identified particles exhibit scaling with the number of constituent quarks. d 3 n M d 3 p M [ d 3 n q d 3 p q (p q p M /2)] 2 d 3 n B d 3 p B [ d 3 n q d 3 p q (p q p B /3)] 3 v 2 (p T ) nv 2 (p T /n) Indication that the system is in a deconfined stage. Plotted vs. transverse kinetic energy (KE T, m T = pt 2 + m2 ) J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

44 Constituent quark scaling at the LHC v 2 scaling with n q (constituent number of quarks) v 2 /n q ratio to pion v 2 /n q Low p T /m T : m T scaling is broken Intermediate p T /m T : Approximate scaling within 20% with number of quarks. Together with the features of the φ-meson v 2 at low p T this suggests that the system evolved through the deconfined (QGP) phase J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

45 Flow at high p T High p T partons loose energy in the medium via gluon radiation. Energy loss and absorbtion depends on path length through medium L. Creates azimuthal anisotropy resembling classic flow. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

46 Flow at high p T v 2 at high transverse momenta 1. Non-zero and positive v 2 up to p T 20 GeV/c sensitivity to the jet quenching and parton energy loss 2. Different v 2 of protons and pions up to p T 8 GeV/c constrain the mechanism of parton fragmentation in medium J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

47 Event-by-event fluctuations Two collisions are never the same! Three collisions with the same impact parameter. The same Reaction Plane. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

48 Event-by-event fluctuations Two collisions are never the same! Spacial asymmetry fluctuates the event-by-event anisotropic flow fluctuates. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

49 Event-by-event fluctuations v k v k Neglecting non-flow terms, the cumulants can be written as (recall c n{2} = vn 2 + δ 2 and c n{4} = vn 4 + δ 4 + 4vn 2 δ 2 + 2δ2 2 2 v n 2 + δ 2 2 ): v n {2} = vn 2, v n {4} = 4 2 vn 2 2 vn 4. For Gaussian fluctuations: For σ v, and up to order σ 2 : v 2 n = σ 2 + v n 2 σ 2 v n {2} = v n v n, v n{4} = v n 1 2 v n Estimate of relative flow fluctuations: σ v = v 2 {4} v 2 {2} v 2 {4} + v 2 {2} σ 2 J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Fluctuations from nucleon distributions v 2

50 Fluctuations from nucleon distributions v 2 fluctuations are significant In forward region are similar to those at midrapidity at all centralities Extend up to p T 8 GeV/c with very similar magnitude J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

51 Fluctuations Fluctuations in the initial shape damped by η/s. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

52 Odd harmonics in fluctuations Odd harmonics arise purely due to fluctuations. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

53 Odd harmonics in fluctuations Odd harmonics arise purely due to fluctuations. Non-zero signal for v 3 {2} and v 3 {4} Together with fluctuations in the 2 nd harmonic provides strong constraint on the initial condition. J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

54 Fluctuations Identified particle v3 I Observed mass splitting for v3 supports expectations from hydrodynamic models I Additional strong constraint on η/s. J. Onderwaater (EMMI,GSI) I Mass dependence up to pt 8 GeV/c I Consistent with zero v3 at higher pt. Collective flow 29 November / 37

55 Summary Multi-particle correlations are an effective method to describe flow Flow is sensitive to the properties of the medium created in heavy-ion collisions. Elliptic flow of charged and identified particles indicates a strong rise of the expension velocity of the medium (radial flow) at RHIC vs LHC. All harmonics are sensitive to η/s, fits of hydro models indicate a strongly coupled phase with low η/3 J. Onderwaater (EMMI,GSI) Collective flow 29 November / 37

Monte Carlo Non-Linear Flow modes studies with AMPT

Monte Carlo Non-Linear Flow modes studies with AMP Daniel Noel Supervised by: Naghmeh Mohammadi 2 July - 31 August 218 1 Introduction Heavy-ion collisions at the Large Hadron Collider (LHC) generate such