1. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page1 Sergei A. Voloshin Wayne State University, Detroit, Michigan for the STAR Collaboration E nergy 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 detector (Main TPC, Forward TPCs, ZDC-SMD). 3.Estimates of flow fluctuations with Monte-Carlo Glauber model. 4. v /  scaling(s).

2. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page2 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 QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page3 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) 2 equations, at least 3 unknowns : v, δ, σ Non-flowFlow fluctuations Non-flow (not related to the orientation of the reaction plane) correlations: -resonance decays -inter and intra jet correlations, etc. Different directions to resolve the problem: - Find methods which suppress / eliminates non-flow or flow fluctuations - Add more equations assuming no new unknowns - Estimate flow fluctuations by other means - Measure flow fluctuations Correlations with large  = |  1 -  2 | Lee-Yang Zeroes (Bessel Transform) Subject of this talk Use equations for v 2 {n}, n>4 Talk by P.Sorensen (STAR)

4. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page4 Data This analysis used the data taken during RHIC Run IV and based on (after all quality cuts) Au+Au 200 GeV ~ 10.6 M Minimum Bias events Au+Au 62 GeV ~ 7 M Minimum Bias events Cu+Cu 200 GeV ~ 30 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 QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page5 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). Relative systematic error at maximum flow ~< 3% (AuAu 200 GeV) ~< 5% (AuAu 62 GeV) ~< 12% (CuCu 200 GeV) ~< 20% (CuCu 62 GeV) Note: significantly larger relative difference between black and blue points in Cu+Cu case compared to Au+Au v 2 from ( Forward TPC * Main TPC ) correlations The difference (blue and red) is due to non-flow assuming that flow fluctuates coherently in the Main and Forward TPC regions

6. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page6 v 2 { FTPC } (p t ), 20-60% centrality There still indications of non-flow contribution in v 2 {FTPC}, especially at high transverse momenta. The green points show the results “AA-pp” [G.Wang (STAR), QM2005] AuAu 200 GeV CuCu 200 GeV Non-flow contribution in v 2 {2}, relatively small in AuAu @200 GeV, increases with p t

7. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page7 CuCu 200 GeV, v 2 { FTPC } (p t ) STAR Preliminary Indicates strong non-flow contribution in v 2 {2} (measured within Main TPC). Non-flow might be still present at high p t in v 2 {FTPC}

8. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page8 Initial eccentricity: “ optical ”, “ standard ”, “ participant ”. “New” coordinate system – rotated, shifted S. Manly, QM2005 “Optical” Glauber calculations:“Monte-Carlo” Glauber model:

9. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page9 Eccentricity fluctuations: ‘ Standard ’ vs ‘ Participant ’ Note: - Relative fluctuations in  part are much smaller than in  std - “participant” eccentricity values are larger compared to “standard”  std ≈  part cos(  Ψ). -In Cu+Cu  Std {4} fails almost at all centralities - The difference between  std and  part is bigger for Cu+Cu than Au+Au - Very weak dependence on collision energy (not shown) - Very small values of  part {4} for central collisions  difficult to use it to rescale v 2 {4} Monte Carlo Glauber nTuples from J. Gonzales (STAR) Black line on the left is  optical used earlier in STAR and NA49 publi- cations. Note that it is about 15% larger than  part almost at all centralities. Main idea: use proper ε {n} to rescale corresponding v 2 {n}:

10. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page10 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 One finds: where : Cu+Cu 200 GeV Au+Au 200 GeV - Fluctuations in  std (green points) are too strong (noticed earlier by R. Snellings.) - Gaussian approximation works rather poorly (no agreement between red and blue points)

11. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page11 Eccentricity fluctuations in AuAu, MC Glauber vs data Flow fluctuations from data are somewhat stronger compared to those in eccentricity (shown in blue) though would be within sytematics. STAR Phys. Rev. C 72 (2005) 014904

12. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page12 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 ) ! ) Systematic error on dn/dy ~10%, similarly on v 2 and S. Hydro results (Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 )are rescaled with  optical Scaling with ε should be used if v 2 ’s in the Main and Forward TPCs are not correlated.

13. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page13 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. (This assumption requires further study with MC Glauber model).

14. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page14 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 QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page15 Conclusions 1. The results for 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 have been estimated from v 2 { 4 } /v 2 { 6 } ratio using Gaussian approximation. 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

16. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page16 Backup slides

17. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page17 v2 { 2 } /eps { 2 } and v2 { 4 } /eps { 4 }

18. S.A. Voloshin STAR QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page18 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 QM’06: Energy and system size dependence of elliptic flow and v 2 /  scaling page19 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