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History of Flow Analysis Methods

History of Flow Analysis Methods. Art Poskanzer. Exploring the secrets of the universe. Color by Roberta Weir. Collective Flow Motivation. Collective Properties of Nuclei Nuclear physics, bulk properties of matter Equation of State Degree of Equilibration Constituents at Early Time

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History of Flow Analysis Methods

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

  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 bounce-off anisotropic radial 1998 Swiatecki 1982 participant-spectator picture J.D. Bowman, W.J. Swiatecki, and C.F. Tsang, LBL-2908 (1973)

  4. Bevalac at Berkeley SuperHILAC Ghiorso 1972 Bevatron Grunder 1974

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

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

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

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

  9. Sphericity py px y pz x qs z (Beam) Reaction plane Best ellipsoid for each event by diagonalizing kinetic energy flow tensor: Major axis and beam axis determine event plane M. Lisa (1999) M. Gyulassy, K.A. Frankel, and H. Stocker, Phys. Lett. 110B, 185 (1982) P. Danielewicz and M. Gyulassy Phys. Lett. B 129, 283 (1983)

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

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

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

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

  14. Squeeze-out bounce squeeze squeeze Schmidt 1986 400 MeV/A Au+Au (MUL 3) Plastic Ball, H.H. Gutbrod et al., PRC 42, 640 (1991) Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990) Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989)

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

  17. Transverse Plane y x <y2> - <x2> ε = <y2> + <x2> Anisotropic Flow as a function of rapidity H. Wieman (2005) around the beam axis self quenching expansion S = π x y

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

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

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

  21. Azimuthal Alignment Ca Nb Au randomized azimuths Q1/M length distribution of Q1-vector normalized by the multiplicity Siemiarczuk 1986 WA80, P. Beckmann et al., Modern Phys. Lett. A2, 163 (1987)

  22. Prediction of positive elliptic flow 2-dimensional transverse sphericity analysis momentum elliptic anisotropy space elliptic anisotropy J.-Y. Ollitrault, PRD 46, 229 (1992), PRD 48, 1132 (1993) 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

  23. Fourier Harmonics Voloshin First to use Fourier harmonics: Event plane resolution correction made for each harmonic Unfiltered theory can be compared to experiment! First to use mixed harmonics First to use the terms directed and elliptic flow for v1 and v2 S. Voloshin and Y. Zhang, hep-ph/940782; Z. Phys. C 70, 665 (1996) See also, J.-Y. Ollitrault, arXiv nucl-ex/9711003 (1997) and J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995)

  24. Azimuthal Flow Angle py px wi negative in backward hemisphere for odd harmonics for n=1: S. Voloshin and Y. Zhang, Z. Phys. C 70, 665 (1996)

  25. First Flow at Brookhaven AGS Forward-Backward subevent ratio backward vn mid forward centrality centrality Q-dist method v1 observed First v2 positive at high energy First v4 observed E877, J. Barrette et al., PRL 73, 2532 (1994)

  26. Move to CERN SPS in Geneva 6 km

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

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

  29. Momentum Conservation v1 No effect on directed flow if acceptance is symmetric about ycm Does not affect elliptic flow if 2nd harmonic event plane is used Other nonflow effects: HBT, resonance decays, final state interactions, 2-track resolution, etc. J.-Y. Ollitrault, Nucl. Phys. A590, 561c (1995) N. Borghini, P. Dinh, J.-Y. Ollitrault, A. Poskanzer, S. Voloshin, PRC 66, 014901 (2002)

  30. Standard Event Plane Method • 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 , pt, or both (with yield weighting) A.M. Poskanzer and S.A. Voloshin, PRC 58, 1671 (1998)

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

  32. STAR (Solenoidal Tracker at RHIC)

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

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

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

  36. Cumulants Four-particle correlation subtracts nonflow to first order nonflow N. Borghini, P.M. Dinh, and J.-Y. Ollitrault, PRC 64, 054901 (2001)

  37. Lee-Yang Zeros Method All-particle correlation subtracts nonflow to all orders • Flow vector projection on arbitrary lab angle,  Sum Generating Function: • Generating function for one  First minimum of |G|2 determines r0 R.S. Bhalerao, N. Borghini, and J.-Y. Ollitrault,Nucl. Phys. A 727, 373 (2003)

  38. Lee and Yang Three Rivers Village Photos by Deena Greer Gagliardi Tsung-Dao Lee Chen Ning Yang 1957 Nobel Prize prediction of non-conservation of parity in weak interactions 1952 Statistical Theory of Phase Transitions

  39. Methods Comparison 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 STAR, J. Adams et al., PRC, submitted (2005)

  40. q-Dist with Nonflow and Fluctuations Sorensen STAR preliminary

  41. Elliptic Flow vs. Beam Energy Wetzler 2004 25% most central mid-rapidity all v2 bounce-off In-plane elliptic flow squeeze-out six decades A. Wetzler (2005)

  42. v2 / HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 NA49, C. Alt et al., Phys. Rev. C 68 034903 (2003) S. Voloshin (2006) S.A. Voloshin and A.M. Poskanzer, Phys. Letters B 474, 27 (2000)

  43. Higher Harmonics Kolb vn v2n/2 more details of the event shape in momentum space J. Adams et al., PRL 92, 062301 (2004)

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

  45. Scaling scaling by number of constituent quarks and integrated v2 plotted vs. trans. kinetic energy Roy Lacy, nucl-ex/0610029 (2006)

  46. RHIC Achievements • Hydrodynamics good • v2 self quenching -> early time • Higher harmonic scaling as v2n/2 • Parton coalescence at intermediate pt

  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

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