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

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

3 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 1998

4 Bevalac at BerkeleySuperHILAC BevatronBevatron Grunder 1974 Ghiorso 1972

5 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

6 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

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

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

9 Sphericity Best ellipsoid for each event by diagonalizing 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)

10 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

11 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

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

13 “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)

14 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 Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991)

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

16 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

17 Transverse Plane y x Anisotropic Flow as a function of rapidity H. Wieman (2005) around the beam axis self quenching expansion ε = + - S = π x y

18 Peripheral Collision x y z x y z (near) Central Collision X Y X Y Centrality Dependence Masashi Kaneta

19 Elliptic Flow Animation by Jeffery Mitchell (Brookhaven National Laboratory)

20 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

21 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

22 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

23 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/ (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

24 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

25 First Flow at Brookhaven AGS 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

26 6 km Move to CERN SPS in Geneva

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

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

29 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, (2002) v1v1 Other nonflow effects: HBT, resonance decays, final state interactions, 2-track resolution, etc. J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)

30 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)

31 RHIC BRAHMS PHOBOS PHENIX STAR AGS TANDEMS Relativistic Heavy Ion Collider (RHIC) at Brookhaven 1 km animation by Mike Lisa 3 km

32 STAR (Solenoidal Tracker at RHIC)

33 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

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

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

36 Cumulants Four-particle correlation subtracts nonflow to first order nonflow N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, (2001)

37 Lee-Yang Zeros Method All-particle correlation subtracts nonflow to all orders R.S. Bhalerao, N. Borghini, and J.-Y. Ollitrault,Nucl. Phys. A 727, 373 (2003) Flow vector projection on arbitrary lab angle,  Generating function for one  First minimum of |G| 2 determines r 0  Sum Generating Function:

Nobel Prize prediction of non-conservation of parity in weak interactions 1952 Statistical Theory of Phase Transitions Lee and Yang Chen Ning YangTsung-Dao Lee Photos by Deena Greer Gagliardi Three Rivers Village

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 q-Dist with Nonflow and Fluctuations Sorensen STAR preliminary

41 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

42 S.A. Voloshin and A.M. Poskanzer, Phys. Letters B 474, 27 (2000) NA49, C. Alt et al., Phys. Rev. C (2003) v 2 /  HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) S. Voloshin (2006)

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

44 scaling by number of constituent quarks plotted vs. trans. kinetic energy STAR, Yan Lu (2006) Particle Identification

45 Scaling Roy Lacy, nucl-ex/ (2006) scaling by number of constituent quarks and integrated v 2 plotted vs. trans. kinetic energy

46 RHIC Achievements Hydrodynamics good v 2 self quenching -> early time Higher harmonic scaling as v 2 n/2 Parton coalescence at intermediate p t

47 Large Hadron Collider at CERN 27 km

48 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 Remove nonflow and fluctuations