1. 1 History of Flow Analysis Methods Art Poskanzer Color by Roberta Weir Exploring the secrets of the universe

2. 2 Collective Flow Motivation Collective Properties of Nuclei Nuclear physics, bulk properties of matter Equation of State Constituents at Early Time Partonic Matter Study the Little Bang in the Laboratory

3. 3 Shock Waves - 1959 Annals of Physics 6, 1 (1959) First prediction of collective flow at high energy Angle depends on the speed of sound which depends on the Eq. of State

4. 4 Shock Waves W. Scheid, H. Muller, and W. Greiner, PRL 32, 741 (1974) M.I. Sobel, P.J. Siemens, J.P. Bondorf, and H.A. Bethe, Nucl. Phys. A251, 502 (1975) G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973)

5. 5 No Shock Waves GSI-LBL, A.M. Poskanzer et al., PRL 35, 1701 (1975) reviewed in H.R. Schmidt, Int. J. Mod. Phys. A6, 3865 (1991) H.G. Baumgardt et al., Z. Physik A 273, 359 (1973) Peaks in tracks in AgCl crystals Poskanzer and Greiner 1984 d  /d  d  /dΩ

6. 6 Shock Waves Again D.H. Rischke, H. Stoecker, and W. Greiner. PRD 42, 2283 (1990) Flow in conical shock wavesAway side jet J. Casalderrey-Solana, E.V. Shuryak, and D. Tracy, arXiv hep-ph/0411315 (2004)

7. 7 Kinds of Flow participant-spectator picture J.D. Bowman, W.J. Swiatecki, and C.F. Tsang, LBL-2908 (1973) Swiatecki 1982 bounce-off anisotropic radial

8. 8 Central collisions of relativistic heavy ions GSI-LBL, J. Gosset et al., PRC 16, 629 (1977) Fireball Coalescence p t vs. y Westfall 1976Gosset 1976

9. 9 Nature 1979 “Relativistic nuclear collisions” from A. M. Poskanzer, Nature 278, 17 (1979) “At still higher densities it is possible that the nucleons might break up into their constituents to produce quark matter” R. Stock and A.M. Poskanzer, Comments on Nuclear and Particle Physics 7, 41 (1977) Stock 1976

10. 10 Inspiration from Hydrodynamics H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980) U Ne Stocker 1995

11. 11 Plastic Ball First 4π detector for nuclear physics: 1980-90 Collective Flow Squeeze-out Plastic Ball, A. Baden et al., Nucl. Instru. and Methods 203, 189 (1982) 1983 Gutbrod 1985

12. 12 Sphericity Best ellipsoid for each event by diagnalizing kinetic energy flow tensor: pzpz (Beam) Reaction plane x y z ss pypy pxpx P. Danielewicz and M. Gyulassy Phys. Lett. B 129, 283 (1983) M. Gyulassy, K.A. Frankel, and H. Stocker, Phys. Lett. 110B, 185 (1982) Major axis and beam axis determine event plane M. Lisa (1999)

13. 13 Polar Flow Angle “The only true signature of collective flow is a clear maximum of dN/d cos  away from  = 0” Directed Flow M. Gyulassy, K.A. Frankel, and H. Stocker, Phys. Lett. 110B, 185 (1982) Gyulassy 1995

14. 14 Discovery of Collective Flow Plastic Ball, Gustafsson et al., PRL 52, 1590 (1984) Non-zero flow angle distribution for Nb, but not Ca dN/dcos  Bevalac 400 MeV/A Ritter 1985

15. 15 Directed Flow Plastic Ball, H.G. Ritter et al., Nucl. Phys. A447, 3c (1985) Au + Au Clear collective flow

16. 16 “Flow” Plastic Ball, K.G.R. Doss et al., PRL 57, 302 (1986) F defined as the slope of the line at mid-rapidity p x /A y/y proj Collective transverse momentum transfer Filter theory to compare with data Flow Beam Energy (MeV/A)

17. 17 Squeeze-out bounce squeeze 400 MeV/A Au+Au (MUL 3) Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989) Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990) Schmidt 1986

18. 18 Squeeze Angle Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991) around the major axis

19. 19 R Projection of 2-dimensional sphericity eigenvectors out-of-plane / in-plane Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)

20. 20 RNRN Squeeze-out Ratio Azimuthal distribution projected out-of-plane / in-plane Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991) around the major axis

21. 21 Transverse Plane y x Anisotropic Flow as a function of rapidity H. Wieman (2005) around the beam axis

22. 22 Transverse Momentum Analysis P. Danielewicz and G. Odyniec, Phys. Lett. 157B, 146 (1985) Second to use the transverse plane First to define 1 st harmonic Q-vector First to use weighting First to use sub-events First to remove auto-correlations Mistake in event plane resolution data mixed events correlation of sub-event planes negative in backward hemisphere Danielewicz

23. 23 Azimuthal Alignment WA80, P. Beckmann et al., Modern Phys. Lett. A2, 163 (1987) length distribution of Q 1 -vector normalized by the multiplicity Q 1 /M randomized azimuths Ca Nb Au Siemiarczuk 1986

24. 24 Prediction of positive elliptic flow At a meeting in Jan ‘93, Jean-Yves told me he was predicting in-plane elliptic flow at high beam energies. I responded that we had just discovered out-of-plane elliptic flow Ollitrault J.-Y. Ollitrault, PRD 46, 229 (1992), PRD 48, 1132 (1993) space elliptic anisotropy momentum elliptic anisotropy 2-dimensional transverse sphericity analysis

25. 25 Fourier Harmonics S. Voloshin and Y. Zhang, hep-ph/940782; Z. Phys. C 70, 665 (1996) First to use Fourier harmonics: Event plane resolution correction made for each harmonic See also, J.-Y. Ollitrault, arXiv nucl-ex/9711003 (1997) First to use the terms directed and elliptic flow for v 1 and v 2 Unfiltered theory can be compared to experiment! First to use mixed harmonics and J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995) Voloshin

26. 26 Azimuthal Flow Angle pxpx pypy for n=1: S. Voloshin and Y. Zhang, Z. Phys. C 70, 665 (1996) w i negative in backward hemisphere for odd harmonics

27. 27 First AGS Flow E877, J. Barrette et al., PRL 73, 2532 (1994) centrality vnvn backward mid forward Forward-Backward subevent ratio centrality Q-dist method v 1 observed First v 2 positive at high energy First v 4 observed

28. 28 First SPS Elliptic Flow NA49, T. Wienold et al., Nucl. Phys. A610, 76c (1996) Forward-Backward subevent resolution centrality Wienold

29. 29 Directed and Elliptic Flow at the SPS NA49, C. Alt et al., PRC 68, 034903 (2003) pionsprotons y ptpt First to use inverse of lab azimuthal distribution for flattening event plane

30. 30 No effect on directed flow if acceptance is symmetric about y cm Does not affect elliptic flow if 2 nd harmonic event plane is used Momentum Conservation N. Borghini, P. Dinh, J.-Y. Ollitrault, A. Poskanzer, S. Voloshin, PRC 66, 014901 (2002) v1v1 Other nonflow effects: HBT, resonance decays, final state interactions, 2-track resolution, etc. J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)

31. 31 Standard Event Plane Method A.M. Poskanzer and S.A. Voloshin, PRC 58, 1671 (1998) Define 2 independent groups of particles Flatten event plane azimuthal distributions in lab Correlate subevent planes Calculate subevent plane resolution Calculate event plane resolution Correlate particles with the event plane Correct for the event plane resolution Average over , p t, or both (with yield weighting)

32. 32 RHIC Day One Physics At Santa Fe APS meeting in Oct. 1998 I predicted day one physics would be elliptic flow At the same meeting one RHIC spokesperson predicted that the “effects of elliptic flow will be small at RHIC”

33. 33 StFlowMakers STAR, A.M. Poskanzer and R.J. Snellings (1999)

34. 34 First RHIC Elliptic Flow 130 GeV/A Au+Au 22 k events STAR, K.H. Ackermann et al., PRL 86, 402 (2001) First paper from STAR Data approach hydro for central collisions Snellings Voloshin Poskanzer

35. 35 Other Methods Particle pair-wise correlations PHENIX, K. Adcox et al., PRL 89, 21301 (2002) Streamer Chamber, S. Wang et al., PRC 44, 1091 (1991) no event plane Scalar Product STAR, C. Adler et al., PRC 66, 034904 (2002) similar to standard method

36. 36 q-dist Method STAR, C. Alt et al., PRC 68, 034903 (2003) nonflow effects flow vector multiplicity modified Bessel function no event plane

37. 37 Multi-particle Methods Lee-Yang Zeros R.S. Bhalerao, N. Borghini, and J.-Y. Ollitrault, Nucl. Phys. A 727, 373 (2003) FOPI, N. Bastid et al., arXiv nucl-ex/0504002 (2005) All-particle correlation subtracts nonflow to all orders Streamer Chamber, J. Jiang et al., PRL 68, 2739 (1992) Explicitly shows flow is a multi-particle correlation Cumulants N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, 054901 (2001) Four-particle correlation subtracts nonflow to first order nonflow

38. 38 High p t STAR, J. Adams et al., PRC, submitted (2005) Modified Event Plane Method: Exclude from the event plane particles with |∆  | < 0.5 around highest p t particle: Removes intra-jet correlations at high p t Filimonov 2005 only momentum anisotropy only space anisotropy uncorrelated jets

39. 39 Methods Comparison STAR, J. Adams et al., PRC, submitted (2005) 2-part. methods multi-part. methods Ratio to the Standard Method: Because of nonflow and fluctuations the truth lies between the lower band and the mean of the two bands

40. 40 A. Wetzler (2005) all v 2 six decades Elliptic Flow vs. Beam Energy 25% most central mid-rapidity Wetzler 2004 In-plane elliptic flow squeeze-out bounce-off

41. 41 Mixed Harmonics 2 nd har. event plane N-particle cumulants v 1 {EP 1,EP 2 } v 1 {3}  N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC, 66, 014905 (2002) CERES, S.A. Voloshin, German Physical Society meeting (1998) Removes nonflow Uses best determined event plane STAR, J. Adams et al., PRC submitted (2005) Oldenburg 2005 Tang

42. 42 Resolution for Higher Harmonics square-root of subevent correlation signal to fluctuation noise Same harmonic V 4 vs. 2 nd V 6 vs. 2 nd STAR, J. Adams et al., PRC, submitted (2005) Application of mixed harmonics Removes nonflow

43. 43 Higher Harmonics J. Adams et al., PRL 92, 062301 (2004) more details of the event shape in momentum space Kolb v n  v 2 n/2

44. 44 Particle Identification p t /n v 2 /n STAR preliminary v2v2 ptpt Ω scaling by number of constituent quarks Sorensen STAR, J. Adams et al., PRC, submitted (2005)

45. 45 RHIC Achievements Physics Hydrodynamics good v 2 self quenching -> early time Higher harmonic scaling as v 2 n/2 Parton coalescence at intermediate p t Analysis Differential results: p t, y, and centrality PID

46. 46 Conclusions 25 years of flow analysis development Extract parameters independent of acceptance Standard Method was the most efficient of statistics With RHIC run 4, systematics are more important than statistics Separation in  of particles and plane Mixed harmonics Check for resonance decays Multi-particle correlations -> Lee-Yang Zeros N. Borghini and J.-Y. Ollitrault, PRC 70, 064905 (2004)