1. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page1 It must be something! - Fully Artistic! - Art’s playground for many years - Fun for everyone! Anisotropic Flow Disclaimer: - Not a real review – this is an introduction to Anisotropic Flow: terminology, physics, analysis techniques, achievements and problems, current status of the art. - Many of the most recent results will be discussed in the original talks at this School. - Apologies for not mentioning many good papers on the subject. This talk is based mostly on works where I participated and know the best. Sergei A. Voloshin Wayne State University, Detroit, Michigan

2. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page2 Outline Part I. Physics 1. Introduction. Definitions. 2. Directed flow - Physics of the “wiggle” - Blast wave parameterization - Coalescence I. Directed flow of light nuclei 3. Elliptic flow - General properties. “Early times” - Low Density and “Hydro” Limits - Phase transition - Blast wave. “Mass splitting” - Coalescence II. Constituent quarks. Resonances. - Elliptic flow at high pt’s. 4. Anisotropies and asymmetries - Femtoscopy of anisotropic source - High pt, 2-particle correlations - Global polarization, Parity violation… 5. Can we measure it? - correlations induced by flow - “Non-flow”. Flow fluctuations Part II. Methods and Results 1. Non-flow estimates - From the “resolution plot” - Azimuthal correlations in pp and AA 2. Multiparticle correlations - 4-particle cumulants. Methods. - Non-flow and flow fluctuations - Mixed harmonics. 3-particle correlations. - Distributions in q-vector - Detector effects 3. Main results - Reaching the hydro limit - Mass splitting - Constituent quark scaling - Elliptic flow at high pt - v 1 and higher harmonics - other 4. Conclusion

3. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page3 Term “flow” does not mean necessarily “hydro” flow – used only to emphasize the collective behavior  multiparticle azimuthal correlation. Newer trend: “event anisotropy” Anisotropic flow Anisotropic flow  correlations with respect to the reaction plane Note large orbital angular momen- tum in the system ! No symmetry between “x” and ”-x”, except midrapidity Symmetry between “y” and and ”-y” (Otherwise – parity violation) X Z XZ – the reaction plane Picture: © UrQMD y xxx

4. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page4 How to characterize anisotropic flow? X Z XZ – the reaction plane Picture: © UrQMD Directed flow Elliptic flow Fourier decomposition of single particle (semi) inclusive spectra: Advantages: - Describes different kind of anisotropies in a common way - Possibility to fully correct the results  compare directly with theory and other experiments PYPY PXPX S.V., Y. Zhang hep-ph/9407282 Z.Phys. C70 (1996) 665

5. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page5 Definitions, continued Terminology: -harmonics, not multipoles (dipole, etc. required to describe 2d or 3d distributions) “… v 2 in pp collisions is almost 100% …” “… event anisotropy at high p t, elliptic flow at low p t …” Anisotropic flow  correlations with respect to the reaction plane The situation with definitions is more complicated with two particle spectra measured with respect to the reaction plane. One way: parameterize, consider parameter dependence on pair orientation relative to the reaction plane.

6. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page6 Why are we interested in anisotropic flow? Short answer: to learn more about system properties, evolution dynamics, hadronization – Anisotropic flow – as a measure of interactions in the system. Example: Does hydrodynamic model works? 1992 paper of J.-Y. Ollitrault Before discussing how the anisotropic flow let us set some time scales (in the center of mass frame): Passing time – the time two nuclei pass each other ~ R A /γ Initial transverse size of the system ~ R A Freeze-out time (could be up to a several R A ) Directed flow is predefined at passing time, as at this moment the initial geometry of the system being set. Elliptic flow is mostly defined at the time scale of the initial size of the system for two reasons: -This is the time required for a fast particle to traverse the system -The time after which the spatial anisotropy diminish Collide Au+Au, is it enough to create QGP? Is the system dense enough? What are the Quark & Gluon densities? Does the system equilibrate? What is the initial Temperature? To answer these questions we need to study the system early in the collision - hard (rare) probes: J/Psi, jets, dileptons,… - anisotropic flow ! PRD 46 (1992) 229

7. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page7 Qualitative features of anisotropic flow. X Z XZ – the reaction plane Picture: © UrQMD y x xx Let us try to “catch” the possible physics : Can we describe flow assuming some properties of the collective motion. Directed flow: does it look like particle emission from a)Moving source? b)Screened source (shadowing)? Elliptic flow: -Surface emission? -Anisotropically expanding source? -Rescattering? Among others, a few pictures will be discussed in more detail: a)Blast wave “parameterization” b)Low Density Limit c)Coalescence

8. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page8 Directed flow “wiggle” in cascade models z x rapidity p x, v 1 Snellings, Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803 x rapidity pxpx x Baryon stopping “wiggle” The wiggle is pronounced only at high energies Does the picture contradict FOPI results on different isotope collisions? Snellings, Poskanzer, S.V., nucl-ex/9904003 Radial flow 

9. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page9 Hydro: “antiflow”, “third flow component” Net baryon density Csernai, Rohrich, PLB 458 (1999) 454. Magas, Csernai, Strottman, hep-ph/0010307 Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke, PRC 61 (2000) 024909 rapidity v1v1 flow antiflow

10. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page10 Third flow component as the QGP signal L.P. Csernai, D. Rohrich PRL 458 (1999) 454 The “wiggle” is present only for the QGP EoS. This calculations have been done at 11 AGeV. Would the results change for RHIC?

11. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page11 Interplay of radial and anisotropic (directed) flow T xx rr Interplay of three velocities: 1)Thermal velocity 2)Radial expansion mean velocity 3)Anisotropic (modulation in radial expansion) High pt particles are produced mostly in the red region; low pt particles – in the blue region Solid lines: non-relativistic case Note! Similar formalism can be achieved with totally different interpretation (not requiring thermalization), where the role of Temperature plays mean pt change due to scattering Radial flow velocity – mean radial component of particle velocity Anisotropic flow velocity – the modulation in the above S.V., PRC 55 (1997) 1630 The effect is larger for larger mass

12. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page12 Fitting the real data S.V and E877, Nucl Phys. A638, 455c (1998) Directed flow of protons in Au+Au collisions at E lab =11.4 GeV, 2.6 < y < 2.8

13. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page13 Coalescence I. E877 light nuclei flow. What is needed for the equation above to work? a)“Rare” process b)B=const only if the configuration space density does not depend on the orientation wrt RP Note! The coalescence picture itself can have much larger region of applicability than the equation above. We/I just do not know how to describe coalescence in the case of “not rare processes”. E877 conclusion: Configuration space density increases in the direction of flow. S.V and E877, Nucl Phys A638 (1998) 455c E877 PRC 59(1999) 884 Note v 1 values > 0.5  there must be other non-zero harmonics!

14. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page14 Resonances S.V and E877, Nucl Phys. A638, 455c (1998) X. Dong, S. Esumi, P.Sorensen, N.Xu,Z. Xu, PLB 597(2004)328 Nonaka, Müller, Asakawa, Bass, Fries PRC 69(2004)031902R Elliptic flow: Note: one of the examples of “non-thermal” interpretation of blast wave formulae

15. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page15 Elliptic flow. General properties.  Other similar/same quantities: Ollitrault:  s Heiselberg:  Sorge: A 2 Shuryak: s 2 Note: -- it is not at all trivial what should be used (if any) for higher harmonics (no simple form) -- s 2 parameter in the Blast Wave fit (below) to v 2 (p t ), in general, is a different parameter -- do not confuse initial and final state anisotropy Elliptic flow must vanish if initially the system was created symmetric. Then, at small eccentricities, v 2 ~  “e” -- initialization of energy density; “s” – initialization of entropy density

16. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page16 Sensitivity to “early times” The sensitivity is due to two reasons: a)Decrease in spatial anisotropy b)Decrease in spatial particle density. Time, fm

17. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page17 When the elliptic flow is formed t (fm/c) Zhang, Gyulassy, Ko, PL B455 (1999) 45 Elliptic flow XZ-plane - the reaction plane X Y Sensitive to the physics of constituent interactions (needed to converts space to momentum anisotropy) at early times (free-streaming kills the initial space anisotropy) The characteristic time scale of 2-4 fm is similar in any model: parton cascade, hydro, etc.

18. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page18 Low density limit (called “collisionless” in the original paper of Heiselberg and Levy) Below - my own derivation of Heiselberg’s results Change in the particle flux is proportional to the probability for the particle to interact. Integrations over: a) particle emission point b) Over the trajectory of the particle (time) with weight proportional to the density of other particles --“scattering centers” Particle density at time t assuming free streaming Heiselberg & Levy, PRC 59 (1999) 2716 Note: (x-vt) changes very little over the entire history

19. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page19 First hydro calculations In hydro, where mean free path is by assumption much less than the size of the system, there is no other parameters than the system size (may enter time scales, see below). Then elliptic flow must follow closely the initial eccentricity. J.-Y. Ollitrault, PRD 46 (1992) 229

20. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page20 Centrality dependence S.V. & A. Poskanzer, PLB 474 (2000) 27 “HYDRO limit” Ollitrault: Heinz et al.: Points – RQMD, dashed curve -  (b)

21. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page21 v 2 /  and phase transitions After original ideas of : Sorge, PRL 82 (1999) 2048, Heiselberg & Levy, PRC 59 (1999) 2716 LDLHYDRO

22. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page22 More on “hydro limits” RHIC 160 GeV/A SPS SPS 40 GeV/A b (fm) Suppressed scale! v 2 /  Minimum in v2/  due to softening of the EoS at phase transition

23. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page23 v 2 /  and phase transitions S.V. & A. Poskanzer, PLB 474 (2000) 27 Uncertainties: Hydro limits: slightly depend on initial conditions Data: no systematic errors, shaded area –uncertainty in centrality determinations. Curves: “hand made” E877 NA49 “Cold” deconfinement? What to expect for different nuclei, Cu+Cu? First guess would be: … but there is no such factor in the LDL:

24. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page24 Centrality dependence. Hydro + RQMD. LH8  latent heat = 0.8 GeV/fm^3 Pt slope parameters are about 20% larger in hydro compared to data 200 400 600 800 dN ch /dy Teaney, Lauret, Shuryak nucl-th/0110037 - v 2 increases with dN/dy - Centrality dependence – close to data

25. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page25 v 2 (p t ) dependence. Blast wave model. v 2 (p t ) - Houvinen, Kolb, Heinz, Ruuskanen, S.V., PLB 503 (2001) 58 v 2 (p t ) - STAR Collaboration, PRL 87 (2001) 182301 Elementary source density - Parameters: T – temperature  0 - radial expansion rapidity  2 - amplitude of azimuthal variation in expansion rapidity T rr Note: a)The possibility different interpretation of the parameters (other than “hydro-like”) b)The possibility of different “realization” of the parameter s 2. There is no strict correspondence between this parameter and the shape of the source at freeze-out.

26. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page26 How much s 2 matters? Elementary source density - Parameters: T – temperature  0 - radial expansion rapidity  2 - amplitude of azimuthal variation in expansion rapidity STAR T (MeV) 135  20100  24 0.0 0.04  0.01 S2S2 00 aa 0.52  0.020.54  0.03 0.09  0.02 0.04  0.01 dashed solid - model fits data well - shape (s 2 parameter) agrees with the interferometry measurements (see below) under assumption that flow velocity field is normal to the surface

27. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page27 v 2 (p t ). “Mass splitting”. Dependence on the EoS. “Mass splitting” is stronger for the QGP EoS. But qualitatively such a mass dependence will be present in any model, for example, in the constituent quark coalescence picture (discussed below) (heavier particle  larger difference in constituent quark momenta) P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen, S.V., PLB503, 58, 2001;

28. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page28 Constituent quark model + coalescence Only in the intermediate region (rare processes) coalescence can be described by :  Taking into account that in coalescence and in fragmentation, there could be a region in quark p t where only few quarks coalesce, but give hadrons in the hadron p t region where most hadrons are produced via coalescence. In the low p t region the density is large and most quarks coalesce: N hadron ~ N quark In the high pt region fragmentation eventually wins: R. Fries coalescence fragmentation Low p t quarks High p t quarks S.V., QM2002 D. Molnar, S.V., PRL 2003 Side-notes: a) more particles produced via coalescence rather than parton fragmentation  larger mean p t … b)  higher baryon/meson ratio c)  lower multiplicity per “participant” -> D. Molnar, QM2004 -> Bass, Fries, Müller, Nonaka; Levai, Ko; … -> Eremin, S.V.

29. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page29 Elliptic flow due to jet quenching Gyulassy, Vitev & Wang, PRL 86 (2001) 2537 R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003 Easier “escape” in the x direction  “in-plane” particle emission

30. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page30 Elliptic flow in absorption model Hard shell Hard sphere Woods-Saxon Hard shell == box density profile (+) extreme quenching E. Shuryak, nucl-th/0112042 Hard sphere == -”- (+) realistic quenching Woods-Saxon == WS density profile (+) realistic quenching L Probability to “escape”: STAR, PRL 93 (2004) 252301

31. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page31 New possibilities Anisotropies and asymmetries 1.HBT with respect to the reaction plane 2.Non-identical particle correlations with respect to the reaction plane 3.High pt 2-particle correlation wrt reaction plane 4.Global polarization in AA 5.Parity violation

32. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page32 Hanbury Brown – Twiss interferometry of an anisotropic source Proposed: S.V. & W. Cleland, PRC 53 (1996) 896; PRC 54(1996) 3212 Further technique developments : U. Wiedemann, U. Heinz, M. Liza First attempt to measure : D. Miskowiec, E877, QM ’95 First and subsequent real measurements : M. Lisa et al., E895, STAR Let us measure the geometry of anisotropic source! x y Can we see the evolution?

33. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page33 T=100 MeV,  0  R=11.7 fm,  =2.2 fm/c  a  s 2  =0.037 Blast wave model : Same parameters fit R(  ) and v  (p T,m) Hanbury Brown – Twiss interferometry of an anisotropic source STAR PRL 93(2004)012301 STAR PRC 71(2005)044906

34. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page34 azHBT S.V. LBNL 1998 annual report # R20 http://ie.lbl.gov/nsd1999/rnc/RNC.htm RQMD v 2.3, AuAu @ RHIC In this picture at high energies /high p t, the relative difference between out-of-plane size and in-plane size only increases.

35. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page35 azHBT-2 IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216 Note “out-of-phase” R side modulations for k=0 case. Should we try very low k T at RHIC?

36. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page36 Do different particles freeze-out at the same place?

37. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page37 Non-identical 2-particle correlations S.V., R. Lednicky, S. Panitkin, Nu Xu, PRL 79 (1997) 4766

38. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page38 2-particle correlations wrt RP x – azimuthal angle, transverse momentum, rapidity, etc. J. Bielcikova, P. Wurm, K. Filimonov S. Esumi, S.V., PRC, 2003 “a” == “trigger particle” CERES, PRL 92(2004)032901 Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination Approach: - “remove” flow contribution - parameterize the shape of what is left - study RP orientation dependence of the parameters STAR, PRL 93 (2004) 252301

39. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page39 Parity, CP- violation, global polarization… D. Kharzeev, hep-ph/0406125 : Emission of positive (negative) pions could be asymmetric along the system angular momentum Liang, Wang, nucl-th:0410079. PRL S.V. nucl-th:0410089 Large orbital momentum of the system can be transformed into particle spin momentum  global polarization Observing parity (CP) violation with anisotropic flow techniques Kharzeev, Pisarski, Tytgat, PRL 81 (1998) 512 Kharzeev, Pisarski, PRD 61 (2000) 111901 S.V. PRC 62 (2000) 044901 S.V. PRC 70 (2004) 057901 Parity violation Global polarization “Oriented” DCC Asakawa, Minakata, Müller, nucl-th/0212070 Negative elliptic flow of neutral pions

40. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page40 How one would measure flow?

41. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page41 Flow induced correlations E877, PRL 73, 2532 (1994)

42. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page42 “Differential flow”. First observation of v 2 > 0 Distribution of hits in the silicon pad detector wrt RP determined by calorimeters. E877, PRC 55 (1997) 1420  n – n-th harmonic Event Plane

43. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page43 End of the ideal world: “Non-flow”, flow fluctuations, … “ Non-flow” – azimuthal correlations of any other origin except the correlation with respect to the reaction plane. It combines the possible contributions from resonance decay, inter and intra jet correlations, etc. An example: Flow   “non-flow” Effect of flow fluctuations Other possibilities fro flow fluctuations: fluctuation in the initial geometry, in multiplicity at the same geometry, etc. Not perfect azimuthal acceptance  not flat Event Plane distribution. “Flattening of the reaction plane”. Approximate and exact solutions to the problem. Each one by itself presents little problem, but taken at the same time, it is the major problem we fight during the last years.

44. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page44 Part I. The End. Part II. Methods and Results 1. Non-flow estimates - From the “resolution plot” - Azimuthal correlations in pp and AA 2. Multiparticle correlations - 4-particle cumulants. Methods. - Non-flow and flow fluctuations - Mixed harmonics. 3-particle correlations. - Distributions in q-vector - Detector effects 3. Main results - Reaching the hydro limit - Mass splitting - Constituent quark scaling - Elliptic flow at high pt - v1 and higher harmonics - other 4. Conclusion

45. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page45 EXTRA

46. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page46 Mixed harmonic technique or 3-particle correlations a > 0  preferential emission along the angular momentum The sign can vary event by event, a~Q/N , where Q is the topological charge, |Q|=1,2,…  at dN/dy~100, |a|~1%. And using only one particle instead of the event flow vector projections onto reaction plane Projections on the direction of angular momentum note that for a rapidity region symmetric with respect to the midrapidity v 1 =0 hep-ph/0406311 All effects non sensitive to the RP cancel out! Possible systematics: clusters that flow

47. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page47 Anti-flow from shadowing Anti-flow is developing in more peripheral collisions

48. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page48 Wiggle from uRQMD Marcus Bleicher, Horst Stocker PLB 526, (2002) 309-314 “Rich” dependence on the particle type: baryons, antibaryons, mesons

49. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page49 Such absorption corresponds to suppression for inclusive yield in central collisions about factor of 4-5 b/2R A V2V2 V4V4 Flow due to absorption. v 2, v 4 ; e 2, e 4 See also: nucl-th/0310044 A. Drees, H. Feng, J. Jia would behave quite differently (sign, etc.) WS density, finite absorption Surface emission limit, hard sphere Not clear what should be used for  4