1. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page1 Sergei A. Voloshin Wayne State University, Detroit, Michigan for the STAR Collaboration Energy and system size dependence of charged particle elliptic flow and v 2 /  scaling Outline: 1.Introduction: Elliptic flow and the system initial eccentricity. Flow fluctuations and non-flow. 2.Measuring flow with STAR Main and Forward TPCs. 3.Estimates of flow fluctuations in Monte-Carlo Glauber model and comparison with real data. 4. v /  scaling(s).

2. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page2 Elliptic flow and the system initial geometry Note: uncertainty in the centrality definition - sqrt(s)=130 GeV data: 0.075 < pt < 2.0 GeV/c - sqrt(s)=200 GeV data: 0.15 < pt < 2.0; - the data scaled down by a factor of 1.06 to account for change in (raw) mean pt. - AGS and SPS – no low pt cut - STAR and SPS 160 – 4 th order cumulants - no systematic errors indicated Motivation for the plot: Hydro limits: slightly depend on initial conditions Data: no systematic errors, shaded area –uncertainty in centrality determinations. Curves: “hand made” S.V. & A. Poskanzer, PLB 474 (2000) 27

3. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page3 v 2 {2}, v 2 {4}, non-flow, and flow fluctuations Several reasons for v to fluctuate in a centrality bin: 1)Variation in impact parameter in a centrality bin (taken out in STAR results) 2)Real flow fluctuations (due to fluctuations in the initial conditions or in the system evolution) Different directions to resolve the problem: - Find methods which suppress / eliminates non-flow - Add more equations assuming no new unknowns - Estimate flow fluctuations by other means 2 equations, at least 3 unknowns: v, δ, σ Correlations with large rapidity gaps Subject of this talk Non-flowFlow fluctuations Non-flow (not related to the orientation of the reaction plane) correlations: -resonance decays -inter and intra jet corelations Use equations for v 2 {n}, n>4

4. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page4 Data This analysis used the data taken during RHIC Run IV and based on (after all quality cuts) Au+Au 200 GeV ~ 5.9 M Minimum Bias events Au+Au 62 GeV ~ 7 M Minimum Bias events Cu+Cu 200 GeV ~ 3.5 M Minimum Bias events Cu+Cu 62 GeV ~ 19 M Minimum Bias events Tracking done by two Forward TPCs (East and West) and STAR Main TPC. Tracks used: | η |<0.9 (Main TPC) -3.9 < η < -2.9 (FTPC East) 2.9 < η < 3.9 (FTPC West) 0.15 < pT < 2.0 GeV/c Results presented/discussed in this talk: elliptic flow in the Main TPC region (|η|<0.9) ZDC Barrel EM Calorimeter Magnet Coils ZDC FTPC west Central Trigger Barrel Main TPC Silicon Vertex Tracker FTPC east

5. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page5 Centrality determination In red – real data, In black – simulations (“Monte Carlo Glauber”) Centrality (% Most Central) determined in accordance to Reference Multiplicity – number of tracks in |eta|<0.5 Au+Au at 200 and 62 GeV: from real data taking into account vertex reconstruction inefficiency. Cu+Cu at 200 and 62 GeV: using simulations (matching the high multiplicity ends of real and simulated data). Note significantly larger fluctuations in Cu+Cu !

6. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page6 Shown in black are results obtained by correlating two random particles from Main TPC. Non-flow contribution can be large and positive. In blue are results for v 2 in the Main TPC region obtained from correlations (Forward*Main) and (East*West). These results are affected insignificantly by non-flow correlations. Note: significantly larger relative non-flow contribution in Cu+Cu case compared to Au+Au v 2 from (ForwardTPC * MainTPC) correlations | η | < 0.9 (Main TPC) -3.9 < η < -2.9 (FTPC East) 2.9 < η < 3.9 (FTPC West)

7. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page7 Initial eccentricity: “optical”, “standard”, “participant”. “New” coordinate system – rotated, shifted S. Manly, QM2005 “Optical” Glauber calculations:“Monte-Carlo” Glauber model:

8. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page8 Eccentricity fluctuations: ‘Standard’ vs ‘Participant’ Note: - Relative fluctuations in  part are much smaller than in “standard” - In general, “participant” eccentricity values are larger compared to “standard”. -In Cu+Cu  Std {4} fails almost at all centralities - The difference between standard and participant is bigger for Cu+Cu than Au+Au - Very weak dependence on collision energy Monte Carlo Glauber nTuples from J. Gonzales (STAR) Black line on the left is  optical used earlier in STAR and NA49 publications. Note that it is about 15% larger than  part almost at all centralities.

9. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page9 Adding one more equation. Flow fluctuations from v 2 {4}/v 2 {6} Assuming: - non-flow does not fluctuate - non-flow exist only on 2-particle level - Gaussian type of fluctuations - (For the last approximation) small relative fluctuations Non-flow

10. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page10 Relative eccentricity fluctuations (MC Glauber), AuAu vs CuCu Au+Au 200 GeVCu+Cu 200 GeV - Fluctuations in  std (shown in green in left panel) are too strong (noticed earlier by R. Snellings.) - Gaussian approximation for the shape of fluctuations works rather poorly (no agreement between red and blue points)

11. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page11 Relative eccentricity fluctuations in AuAu, MC Glauber vs data Flow fluctuations from data are stronger compared to those in eccentricity (shown in blue) STAR Phys. Rev. C 72 (2005) 014904

12. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page12 Effect of fluctuations in eccentricity If compare to the “original” v 2 /  plot (page 2) note the difference in eccentricity  optical, old (using parameterization made for SPS energies) and  part (  optical, old ~ (1.1– 1.2) *  part ) ! ) No systematic errors are shown in the plot ! Hydro results are rescaled with  optical HYDRO: Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909

13. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page13 v 2 {ZDC-SMD} and eccentricity scaling Au +Au 200 GeV STAR preliminary G. Wang (STAR) QM2005 Note that under assumption that the directed flow of spectator neutrons is not correlated to the elliptic shape of the system at midrapidty, v 2 {ZDC-SMD} should follow  std

14. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page14 v 2 /  scaling Scaling holds rather well, though AuAu 62 GeV results are somewhat higher. Hydro curves are obtained from calculations Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909, made at b=7 fm and rescaled by ‘optical’ eccentricity value. The centrality dependence is not fully reflected by these curves, as it is more ‘flat’ at each given collision energy (very roughly indicated by strait lines)

15. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page15 Conclusions 1.The results for (integrated) elliptic flow at midrapidity in Au+Au and Cu+Cu collisions have been presented for collision energies √s NN = 200 and 62 GeV using correlations of particles in the Main TPC and FTPCs regions. 2.Initial eccentricity and its fluctuations have been studied with Monte Carlo Glauber model. 3.Flow fluctuations has been estimated from v2{4}/v2{6} ratio using Gaussian approximation (though the study of eccentricity fluctuations in Monte Carlo Glauber model show that the accuracy of the Gaussian approximation is about ‘factor of two’). 4.The v 2 /  2 scaling holds well for all four systems (Au+Au and Cu+Cu at different energies) once the fluctuations in eccentricity have been taken into account. v 2 {ZDC-SMD} scales well with  std (final conclusion would require more work with MC Glauber model to understand to which extent spectators are correlated with impact parameter).

16. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page16 Backup slides

17. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page17 Observation of non-flow in azimuthal correlations - In Cu+Cu collisions the azimuthal correlations in the main TPC are dominated by non-flow. -The relative contribution of non-flow is at least 2 times smaller in correlations between Forward and Main TPCs. Main * ForwardMain_a * Main_b FTPC_east * FTPC_west “a” and “b” are two random particles from Main TPC In this kind of plots non-flow correlation contribution should be either flat or slightly increasing

18. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page18 Eccentricity for the ‘standard’ STAR centrality bins AuAu200 CuCu200 No multiplicity weight! Centrality bin 1 2 3 4 5 6 7 8 9 10 Fraction of cross section (%) >80 70-80 60-70 50-60 40-50 30-40 20-30 10-20 5-10 0-5

19. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page19 One should use  {2}, not eps! It could improve the agreement… What about v2{4}/  {4}?

20. S.A. Voloshin STAR ICHEP 2006, Moscow, RUSSIA, July 26 – August 2, 2006page20 Eccentricity, Monte-Carlo Glauber, all four systems. Black line on the left is  optical used earlier in STAR and NA49 publications. Note that it is about 15% larger than  part almost at all centralities. Note large difference between Au+Au and Cu+Cu systems and almost no dependence on energy