Rachid Nouicer Brookhaven National Laboratory (BNL)

1. 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. 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 ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER 8 institutions with 46 collaborators 9 PhDs in progress

3. Outline What can we learn from flow measurements in Au+Au and Cu+Cu collisions from PHOBOS? • 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

4. Measuring Flow in PHOBOS Large coverage: |h| < 5.4 Octagon Ring counters Ring counter Vertex detector Spectrometer Hit-based method Track-based method PHOBOS: PRL 89, 222301 (2002) PHOBOS: PRC C72, 051901R (2005)

5. Track-based method: Robustness of Measurements of v2 vs. pT Octagon Only Rings Only Statistical errors only • Reaction plane subevents • v2(pT) measured in 0 < h < 1.6 Cu+Cu at 200 GeV PHOBOS 2) 3.0 < |h|< 5.4 3) 2.0 < |h|< 5.4 1) 2.0 < |h|< 3.2 Track-based method Spectrometer Preliminary Octagon and Rings The large separation in h between the reaction plane subevents and the measured region reduces the non-flow correlations in track-based (hit-based) method.

6. Results of Flow Measurements Au+Au and Cu+Cu collisions at RHIC energies • Pseudorapidity dependence • Centrality dependence • Transverse momentum dependence • Energy dependence Full acceptance |h| < 5.4 Mid-rapidity region

7. Au+Au Results: Directed Flow Au+Au Pseudorapidity dependence Au+Au:PHOBOS CollaborationPRL 97, 012301 (2006) v1measured:-broad h range- several energies Observation: - No significant indication of structure near midrapidity

8. Au+Au and Cu+Cu: Elliptic Flow Au+Au v2measured:-broad h range- several energies Observations on v2 of Cu+Cu : - large - similar in shape to Au+Au Cu+Cu Au+Au:PHOBOS CollaborationPRL. 94, 122303 (2005) Preliminary Cu+Cu:PHOBOS CollaborationPRL: nucl-ex/0610037

9. Au+Au and Cu+Cu Results: Elliptic Flow Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037 Statistical errors only Surprise from RHIC:substantial flow signal is observed in Cu+Cu and Au+Au at all energies even for the most central collisions Centrality dependence Au+Au:PHOBOS CollaborationPRL 97, 012301 (2006) Statistical errors only

10. Au+Au and Cu+Cu Results: Elliptic Flow 0-20% 20-40% Preliminary Au+Au Au+Au Preliminary Cu+Cu Cu+Cu Transverse Momentum Dependence • Track-based method 0 < h < 1.6 • v2 vs. pT measured: • two energies • two systems • Observations for the same system: • centrality dependent

11. Energy Dependence of Elliptic Flow 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). Observation: -v2 continues to grow to the highest RHIC energy Interesting to see v2 at LHC?

12. System Comparisons • 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

13. Standard Eccentricity Calculation Standard Eccentricity Statistical errors only PHOBOS CollaborationPRL: nucl-ex/0610037 Cu+Cu 200 GeV Au+Au 200 GeV Statistical errors only 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV PRL: nucl-ex/0610037 PRC C72, 051901R (2005)

14. Eccentricity Calculation Participant Eccentricity Statistical errors only Au+Au 200 GeV Cu+Cu 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV PHOBOS CollaborationPRL: nucl-ex/0610037 PHOBOS CollaborationPRL: nucl-ex/0610037

15. Theorists & PHOBOS since QM2005 2 ε part ε part It has been suggested that v2 may scale as instead of • -Bhalerao, Ollitrault – PLB 641, 260 (2006) • - Ollitrault – private communications (2006) • PHOBOS MC • In Collaboration with Ulrich Heinz

16. Au+Au and Cu+Cu Results: Elliptic Flow Au+Au at 200, 130, 62.4 and 19.6 GeV :PHOBOS CollaborationPRL 97, 012301 (2006) STAR, NA49 and E877 data taken from Phys.Rev. C66 (2002) 034904 with no adjustments Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037 Statistical errors only Cu+Cu at 22.4 GeV PHOBOS Preliminary This suggests that part is the relevant geometric quantity for generating the azimuthal asymmetry

17. Au+Au and Cu+Cu Results: Elliptic Flow Similar area density (1/S)dN/dy and scaled by epart Similar area density (1/S)dN/dy Statistical errors only Statistical errors only v2(pT)/epart of Cu+Cu and Au+Au are similar for the same area density, (1/S)dN/dy Transverse momentum and system size dependence

18. Au+Au and Cu+Cu Results: Elliptic Flow Au+Au vs. Cu+Cu at 62.4 GeV Statistical errors only Npart=80 v2(h)/epart of Cu+Cu and Au+Au (same area density) are similar over full coverage (|h|<5.4) Pseudorapidity dependence and system size dependence Same area density (1/S)dN/dy and Scaled by epart Au+Au vs. Cu+Cu at 200 GeV Statistical errors only Npart=82

19. Extended Longitudinal Scaling of Elliptic Flow Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037 Scaled by epart Same area density (1/S)dN/dy Statistical errors only PHOBOS Au+Au and Cu+Cu systems at 200 and 62.4 GeV exhibit the same extended longitudinal scaling when epart and (1/S)dN/dy are taken into consideration Au+Au at 200, 130, 62.4 and 19.6 GeV :PHOBOS CollaborationPRL 97, 012301 (2006) Scaled by epart Same centrality (40%) Statistical errors only PHOBOS

20. Importance of Fluctuations in Initial Eccentricity • Participant eccentricity scaling allows consistent description of Cu+Cu and Au+Au v2 systematics • This points to the importance of fluctuations in initial geometry (which are ignored for estd) • We can test this directly measuring v2 fluctuations:See talk by Constantin Loizides on Saturday, 4:20pm, Parallel 2.4

21. Summary • v2 of Cu+Cu is large, similar in pseudorapidity shape to Au+Au • v2 (|h|<1 and 0-25% centrality) continues to grow from SPS to RHIC energies • Scaling of v2/ 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