S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August System size, energy and  dependence of directed and elliptic flow Steven Manly (Univ. of Rochester) For the PHOBOS Collaboration

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Collaboration meeting, BNL October 2002 Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Shaun Wyngaardt, Bolek Wysłouch ARGONNE NATIONAL LABORATORYBROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOWMASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWANUNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLANDUNIVERSITY OF ROCHESTER Collaboration meeting in Maryland, 2003

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Flow in PHOBOS Ring counter Octagon Spectrometer arm Paddle trigger Vertex detector

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Flow in PHOBOS Subevent A

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August with azimuthal pattern of hits in another part of the detector Flow in PHOBOS Subevent B

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Or with tracks identified in the spectrometer arms Flow in PHOBOS Tracks

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Separation of correlated subevents typically large in  Flow in PHOBOS

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August For directed flow we use subevents that are symmetric about  =0 Flow in PHOBOS Subevent B Subevent A

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Differential flow has proven to be a useful probe of heavy ion collisions:  Centrality  p T  Pseudorapidity  Energy  System size  Species Probing collisions with flow

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Au-Au – directed flow Au-Au 19.6 GeV h ± Au-Au 62.4 GeV h ± Au-Au 130 GeV h ± Au-Au 200 GeV h ± Update of directed flow result first shown at QM2004 Similar (2-subevent) technique Added 62.4 GeV data Confirmed with mixed harmonic analysis See poster by A. Mignerey in Poster 1, section 2, number 47 PHOBOS preliminary 0-40% centrality

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) PHOBOS Au-Au, h ± 0-40% centrality Au-Au – elliptic flow

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) PHOBOS Au-Au, h ± 0-40% centrality Au-Au – elliptic flow ó Recent theoretical progress in understanding v 2 (η). See, for example:  M.Csanád, T.Csörgó, B.Lörstad, Nucl. Phys. A742 (2004) 80 [nucl-th/ ]  U.Heinz, P.F.Kolb, J.Phys. G30 (2004) S1229 [nucl-th/ ]  T.Hirano, M.Isse, Y.Nara, AOhnishi, and K Yoshino, nucl-th/

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Directed flow exhibits extended longitudinal scaling, i.e., approximate rest frame of nucleus. Directed flow – extended longitudinal scaling Systematic errors only PHOBOS preliminary h ±, Au-Au 0-40% centrality  '=|  |-y beam v1v1

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Au-Au data, h ± 0-40% centrality  '=|  |-y beam Elliptic flow exhibits striking extended longitudinal scaling PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) v2v2 Elliptic flow – extended longitudinal scaling Systematic errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August  ’=|  |-y beam Elliptic flow exhibits striking extended longitudinal scaling PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) If so, it is an unfortunate coincidence that we saturate v 2 right at the highest energy density we can achieve: no break in slope Mid-rapidity, 200 GeV, Au-Au Reached the hydro limit?  '=|  |-y beam v2v2 Elliptic flow – extended longitudinal scaling Au-Au data, h ± 0-40% centrality Systematic errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Differential flow has proven to be a useful probe of heavy ion collisions:  Centrality  p T  Pseudorapidity  Energy  System size  Species Elliptic flow – Cu-Cu results

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – Cu-Cu results  Cu flow is large  Track- and hit-based results agree (200 GeV)  ~20-30% rise in v 2 from 62.4 to 200 GeV PHOBOS preliminary Cu-Cu, h ± Hit based 62.4 GeV Hit based 200 GeV Track based 200 GeV

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – Cu-Cu results Cu-Cu v 2 (η) shape reminiscent of Au-Au PHOBOS preliminary Cu-Cu, 62.4 GeV, h± 0-40% centrality PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – Cu-Cu results Longitudinal scaling reminiscent of Au-Au PHOBOS preliminary Cu-Cu, h ± v2v2  '=|  |-y beam Cu-Cu collisions also exhibit extended longitudinal scaling statistical errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Standard eccentricity (  standard ) x System size and eccentricity Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems Centrality measure  N part   Paddle signal, ZDC, etc. MC simulations What is the relevant eccentricity for driving the azimuthal asymmetry?

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Fluctuations in eccentricity are important for small A. System size and eccentricity Participant eccentricity (  part ) x Standard eccentricity (  standard ) x Two possibilities

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Fluctuations in eccentricity are important for the Cu-Cu system. System size and eccentricity Must use care in doing Au-Au to Cu-Cu flow comparisons. Eccentricity scaling depends on definition of eccentricity.

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – v 2 scaling  Expect / ~ constant for system at hydro limit.  Note the importance of the eccentricity choice. h ± 1  statistical and systematic errors added in quadrature h ±

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – v 2 scaling h ± 1  statistical and systematic errors added in quadrature h ± Given other similarities between Au-Au and Cu-Cu flow, perhaps this is evidence that  part is (close to) the relevant eccentricity for driving the azimuthal asymmetry

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – v 2 scaling Expectin “low density limit”.

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – v 2 scaling Approximate “LDL” scaling observed.  Caution: we used  part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au.  Scale v 2 (  ) to ~v 2 (y) (10% lower)  Scale dN/d  to be ~dN/dy (15% higher)

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – v 2 scaling Approximate “LDL” scaling observed. Points for STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) with no adjustments  Caution: we used  part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au.  Scale v 2 (  ) to ~v 2 (y) (10% lower)  Scale dN/d  to be ~dN/dy (15% higher)

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – system dependence Eccentricity difference is important for same centrality selection. V 2 (p T ) for Cu-Cu is similar v 2 (p T ) for Au-Au when scaled by  part PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August v 2 for Cu-Cu is ~20% smaller than v 2 for Au-Au plotted 0-40% centrality. Drops another ~20% if scaled by ratio PHOBOS 62.4 GeV h ± 0-40% centrality Elliptic flow – system dependence preliminary PHOBOS 200 GeV h ± 0-40-% centrality Statistical errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August This data shows v 2 does not scale linearly with A as expected by AMPT (factor of 3) AMPT multi-phase transport model (Chen and Ko, nucl-th/ ) PHOBOS 62.4 GeV h ± 0-40% centrality Elliptic flow – system dependence preliminary PHOBOS 200 GeV h ± 0-40-% centrality Statistical errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Au-Au directed flow including the new 62.4 GeV data. PHOBOS preliminary Au-Au 19.6 GeV Au-Au 62.4 GeV Au-Au 130 GeVAu-Au 200 GeV

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Cu-Cu elliptic flow large. Similar in shape to Au-Au. PHOBOS preliminary Cu-Cu, 62.4 GeV, h± 0-40% centrality PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to reaching hydro limit. PHOBOS Au-Au, h ± PHOBOS preliminary Cu-Cu, h ± v2v2  '=|  |-y beam v2v2 statistical errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Eccentricity definition very important for small systems. h ± 1  statistical and systematic errors added in quadrature h ±

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for  part may imply that  part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry.

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Conclusions  Au-Au directed flow results updated.  Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to reaching hydro limit.  Eccentricity definition very important for small systems.  Cu-Cu elliptic flow large. Similar in shape to Au-Au.  v 2 (p T ) is similar in Au-Au and Cu-Cu systems when  part is used.  Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for  part may imply that  part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry.

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Backup Slides

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow subevent regions Cu-Cu, 200 and 62.4 GeV and Au-Au, 19.6, 62.4, 130 and 200 GeV: 0.1<| η |<3.0 (use 0.5<|η|<3.0 and 1.0<|η|<3.0 for systematic studies) Regions used to determine reaction plane and resolution.

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Directed flow subevent regions Regions used to determine reaction plane and resolution. v 1 baseline Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0 (use 1.5<|η|<2.5 and 3.5<|η|<5.0 for systematic studies) v 1 mixed harmonic Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0 for the first harmonic part and 0.1<|η|<3.0 for the second harmonic part

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Baseline analysis overlaid with new PHOBOS mixed harmonic analysis Shows non-flow correlations small Mixed harmonic method: STAR collaboration, Phys. Rev. C 72 (2005) PHOBOS preliminary h ± Au-Au Au-Au update – directed flow PHOBOS preliminary h ± Au-Au

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Au-Au update – directed flow 62.4 GeV results are particularly good due to:  large directed flow  large number of tracks/event  large elliptic flow (for mixed harmonic) STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/ Preliminary PHOBOS and STAR results agree well at 62.4 GeV except at highest |  | 62.4 GeV Au-Au, h ±

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Au-Au update – directed flow 62.4 GeV directed flow comparison STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Au-Au update – directed flow Comparison of directed flow results at 62.4 GeV Estimated by PHOBOS from weighted average of STAR data in multiple centrality bins We used the centrality dependence of STAR’s results to estimate the STAR results in the 10-50% centrality bin 62.4 GeV Au-Au, h ± Discrepancy at high η possibly due to differences in low momentum cutoff?

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Comparison of preliminary PHOBOS 200 GeV v 1 with published STAR results. Plots identical except for STAR centrality selection. Au-Au update – directed flow STAR 200 GeV results from Phys. Rev. C 72 (2005)

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Only statistical errors shown Au+Au data (0-40% central) Au-Au update – elliptic flow PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005)

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August Elliptic flow – Cu-Cu results Models from Hirano et al., nucl-th/ , probably see more later this session Cu-Cu more like Hydro than JAM hadron string cascade model Here JAM uses a 1 fm/c formation time. Hydro (160) has kinetic freezeout temperature at 160 MeV preliminary 200 GeV Cu-Cu preliminary 200 GeV 15-25% Cu-Cu Statistical errors only

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August System size and eccentricity Au-Au Cu-Cu PHOBOS-Glauber MC preliminary Mean eccentricity shown in black