1 1 Rachid Nouicer - BNL PHOBOS QM Energy and Centrality Dependence of Directed and Elliptic Flow in Au+Au and Cu+Cu Collisions at RHIC Energies Rachid Nouicer Brookhaven National Laboratory (BNL) For the PHOBOS Collaboration

2 2 Rachid Nouicer - BNL PHOBOS QM PHOBOS Collaboration Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Bolek Wysłouch 8 institutions with 46 collaborators 9 PhDs in progress 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

3 3 Rachid Nouicer - BNL PHOBOS QM Outline Measuring flow in PHOBOS - Directed and elliptic flow in Au+Au and Cu+Cu collisions - Dependence on centrality, transverse momentum, pseudorapidity, energy and system size Interplay between initial state collision geometry and elliptic flow - Emphasis on simple scaling features of the data What can we learn from flow measurements in Au+Au and Cu+Cu collisions from PHOBOS?

4 4 Rachid Nouicer - BNL PHOBOS QM Measuring Flow in PHOBOS Hit-based method Ring counter Vertex detector Large coverage: |  | < 5.4 Ring counters Octagon Spectrometer Track-based method PHOBOS: PRC C72, R (2005) PHOBOS: PRL 89, (2002)

5 5 Rachid Nouicer - BNL PHOBOS QM Track-based method: Robustness of Measurements of v 2 vs. p T The large separation in  between the reaction plane subevents and the measured region reduces the non-flow correlations in track-based (hit-based) method. Octagon and Rings Rings Only Octagon Only 1) 2.0 < |  |< 3.2 2) 3.0 < |  |< 5.43) 2.0 < |  |< 5.4 Reaction plane subevents v 2 (p T ) measured in 0 <  < 1.6 Spectrometer Statistical errors only Track-based method Cu+Cu at 200 GeV PHOBOS Preliminary

6 6 Rachid Nouicer - BNL PHOBOS QM Results of Flow Measurements  Pseudorapidity dependence  Centrality dependence  Transverse momentum dependence  Energy dependence Au+Au and Cu+Cu collisions at RHIC energies Full acceptance |  | < 5.4 Mid-rapidity region

7 7 Rachid Nouicer - BNL PHOBOS QM Au+Au Results: Directed Flow Pseudorapidity dependence Au+Au: PHOBOS Collaboration PRL 97, (2006) v 1 measured: - broad  range - several energies Observation: - No significant indication of structure near midrapidity Au+Au

8 8 Rachid Nouicer - BNL PHOBOS QM Au+Au and Cu+Cu: Elliptic Flow Au+Au Au+Au: PHOBOS Collaboration PRL. 94, (2005) Cu+Cu: PHOBOS Collaboration PRL: nucl-ex/ Cu+Cu Preliminary v 2 measured: - broad  range - several energies Observations on v 2 of Cu+Cu : - large - similar in shape to Au+Au

9 9 Rachid Nouicer - BNL PHOBOS QM Au+Au and Cu+Cu Results: Elliptic Flow Centrality dependence Au+Au: PHOBOS Collaboration PRL 97, (2006) substantial flow signal is observed in Cu+Cu and Au+Au at all energies even for the most central collisions Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/ Statistical errors only

10 Rachid Nouicer - BNL PHOBOS QM Au+Au and Cu+Cu Results: Elliptic Flow Transverse Momentum Dependence Preliminary Au+Au 0-20%20-40% Cu+Cu v 2 vs. p T measured: - two energies - two systems Track-based method 0 <  < 1.6 Observations for the same system: - centrality dependent

11 Rachid Nouicer - BNL PHOBOS QM Energy Dependence of Elliptic Flow Observation: - v 2 continues to grow to the highest RHIC energy Interesting to see v 2 at LHC? We add PHOBOS data (Au+Au at 19.6, 62.4, 130 and 200 GeV) to the data compiled by Nicolas Borghini and Urs Wiedemann, J.Phys.G in preparation (Private communication).

12 Rachid Nouicer - BNL PHOBOS QM  Compare Au+Au vs. Cu+Cu Collisions Probe interplay of initial geometry and final state azimuthal anisotropy Study consequences of early thermalization and collectivity  Emphasis on simple scaling features of the data System Comparisons

13 Rachid Nouicer - BNL PHOBOS QM Statistical errors only Standard Eccentricity Calculation Standard Eccentricity PHOBOS Collaboration PRL: nucl-ex/ Au+Au 200 GeV Cu+Cu 200 GeV Statistical errors only 200 GeV PRL: nucl-ex/ Au+Au 200 GeV Cu+Cu 200 GeV PRC C72, R (2005)

14 Rachid Nouicer - BNL PHOBOS QM Eccentricity Calculation Participant Eccentricity PHOBOS Collaboration PRL: nucl-ex/ Au+Au 200 GeV Cu+Cu 200 GeV Statistical errors only PHOBOS Collaboration PRL: nucl-ex/ Cu+Cu 200 GeV Au+Au 200 GeV

15 Rachid Nouicer - BNL PHOBOS QM It has been suggested that v 2 may scale as instead of - Bhalerao, Ollitrault – PLB 641, 260 (2006) - Ollitrault – private communications (2006) Theorists & PHOBOS since QM2005 In Collaboration with Ulrich Heinz 2 part ε ε PHOBOS MC

16 Rachid Nouicer - BNL PHOBOS QM Au+Au and Cu+Cu Results: Elliptic Flow STAR, NA49 and E877 data taken from Phys.Rev. C66 (2002) with no adjustments This suggests that  part is the relevant geometric quantity for generating the azimuthal asymmetry Statistical errors only Au+Au at 200, 130, 62.4 and 19.6 GeV : PHOBOS Collaboration PRL 97, (2006) Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/ Cu+Cu at 22.4 GeV PHOBOS Preliminary

17 Rachid Nouicer - BNL PHOBOS QM Transverse momentum and system size dependence Au+Au and Cu+Cu Results: Elliptic Flow Similar area density (1/S)dN/dy Statistical errors only v 2 (p T )/  part of Cu+Cu and Au+Au are similar for the same area density, (1/S)dN/dy Similar area density (1/S)dN/dy and scaled by  part Statistical errors only

18 Rachid Nouicer - BNL PHOBOS QM Au+Au and Cu+Cu Results: Elliptic Flow Pseudorapidity dependence and system size dependence Au+Au vs. Cu+Cu at 200 GeV Same area density (1/S)dN/dy and Scaled by  part Statistical errors only Au+Au vs. Cu+Cu at 62.4 GeV v 2 (  )/  part of Cu+Cu and Au+Au (same area density) are similar over full coverage (|  |<5.4) Statistical errors only N part =80 N part =82

19 Rachid Nouicer - BNL PHOBOS QM Extended Longitudinal Scaling of Elliptic Flow Scaled by  part Same centrality (40%) Same centrality (40%) Statistical errors only PHOBOS Scaled by  part Same area density (1/S)dN/dy Same area density (1/S)dN/dy Au+Au and Cu+Cu systems at 200 and 62.4 GeV exhibit the same extended longitudinal scaling when  part and (1/S)dN/dy are taken into consideration Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/ Statistical errors only PHOBOS Au+Au at 200, 130, 62.4 and 19.6 GeV : PHOBOS Collaboration PRL 97, (2006)

20 Rachid Nouicer - BNL PHOBOS QM Importance of Fluctuations in Initial Eccentricity Participant eccentricity scaling allows consistent description of Cu+Cu and Au+Au v 2 systematics This points to the importance of fluctuations in initial geometry (which are ignored for  std ) We can test this directly measuring v 2 fluctuations: See talk by Constantin Loizides on Saturday, 4:20pm, Parallel 2.4

21 Rachid Nouicer - BNL PHOBOS QM Summary v 2 of Cu+Cu is large, similar in pseudorapidity shape to Au+Au v 2 (|  |<1 and 0-25% centrality) continues to grow from SPS to RHIC energies Scaling of v 2 /  part of Cu+Cu and Au+Au for the same area density:- as a function pseudorapidity - as a function of centrality - as a function of transverse momentum this suggests that  part is the relevant geometric quantity for generating the azimuthal asymmetry

22 Rachid Nouicer - BNL PHOBOS QM Auxiliary Slides

23 Rachid Nouicer - BNL PHOBOS QM Cu-Cu results: Elliptic Flow Centrality dependence Plot with systematic errors

24 Rachid Nouicer - BNL PHOBOS QM Cu-Cu results: Elliptic Flow Centrality dependence Cu+Cu at 22.4 GeV preliminary Au+Au at 19.6 GeV : PHOBOS Collaboration PRL 97, (2006)

25 Rachid Nouicer - BNL PHOBOS QM Variations in: –  NN –skin depth a, –nuclear radius R A, –min N-N separation d  PHOBOS Submitted PRL Variations in: –Individual nucleon density profiles –different weighting. Cu+Cu and Au+Au How robust is Glauber MC + calculation? PBOBOS MC

26 Rachid Nouicer - BNL PHOBOS QM Scaling using Integrated v 2 Scaling works over a broad range for charged hadrons (h ± ) Scaled v 2 vs. p T of Cu+Cu and Au+Au collisions at the same energy indicate system size independence 200 GeV 62.4 GeV PHOBOSPHOBOS Preliminary Preliminary PHENIX Collaboration: Nuclear Physics A774, (2006).

27 Rachid Nouicer - BNL PHOBOS QM Extended Longitudinal Scaling of Elliptic Flow Cu+Cu at 22.4 GeV preliminary Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/

28 Rachid Nouicer - BNL PHOBOS QM Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Flow in PHOBOS Subevent A

29 Rachid Nouicer - BNL PHOBOS QM with azimuthal pattern of hits in another part of the detector Subevent B Flow in PHOBOS