Elliptic flow at RHIC

1. Elliptic flow at RHIC Raimond Snellings

2. y x py px Why is elliptic flow interesting? coordinate space • Coordinate space configuration anisotropic (almond shape) however, initial momentum distribution isotropic (spherically symmetric) • Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in pp) • Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow Momentum space

3. Time evolution in a ideal hydrodynamic model calculation • Elliptic Flow reduces spatial anisotropy -> shuts itself off

4. Main contribution to elliptic flow early in the collision Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45

5. STAR PRL 86, (2001) 402 PHOBOS || < 1.3 0.1 < pt < 2.0 v2 versus centrality PHENIX First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with hydrodynamic model predictions for v2 up to mid-central collisions

6. Identified particle v2 • Typical pt dependence • Heavy particles more sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS Fluid cells expand with collective velocity v, different mass particles get different Dp

7. Identified particle v2 (130 GeV) The STAR Collaboration, Phys. Rev. Lett. 87 (2001) 182301 Source not spherical in coordinate space at freeze-out!

8. v2(pt,mass) 130 vs. 200 GeV • Identified particle v2 at 130 and 200 GeV very close Preliminary

9. PHENIX and STAR PHENIX STAR Preliminary

10. Preliminaryv2200 Final v2130 PHOBOS v2(h) Only a little increase average over all centrality (Npart ~200) 200 130 Inkyu Park Talk Centrality dependence study is limited by statistics

11. v2(pt) for high pt particles M. Gyulassy, I. Vitev and X.N. Wang http://www.lbl.gov/nsd/annual/rbf/nsd1998/rnc/RNC.htm R17. Event Anisotropy as a Probe of Jet QuenchingR.S and X.-N. Wang R.S, A.M. Poskanzer, S.A. Voloshin, STAR note, nucl-ex/9904003

12. Charged particle v2 at high-pt STAR preliminary STAR preliminary Above 6 GeV we do not have a reliable answer (yet) what the real flow contribution is PHENIX preliminary

13. What have we learned from elliptic flow at RHIC • L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (hep-ph/0202025). • U. Heinz: resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (hep-ph/0109006). • E. Shuryak: probably the most direct signature of QGP plasma formation, observed at RHIC (nucl-th/0112042). • QGP conclusions are model dependent and in my opinion these models are not sufficiently constrained yet. (RS)

14. <r> [c] Tth [GeV] Excitation Functions

15. Elliptic flow; excitation function NA49 nucl-ex/0303001 preliminary

16. v2(pt) SPS-RHIC • Surprisingly close! • <pt> pions 158 A GeV ≈ 300 MeV • <pt> charged particles 200 GeV ≈ 500 MeV • Integrated v2 mainly driven by <pt> Preliminary

17. Why does hydro describe v2 at RHIC and not at the SPS?

18. The “Reaction Plane” • Anisotropic flow ≡ azimuthal correlation with the reaction plane • Experimentally the reaction plane Yr is unknown • Can introduce “non-flow” contributions

19. Event plane resolution • Event plane resolution  N * v22 • Most non flow contributions v2 1/N • Kovchegov and Tuchin: N = Nwounded • Non flow contribution will be constant in this variable. Dashed red line estimate of non-flow in first STAR flow paper STAR, PRL 86, (2001) 402, Nucl. Phys. A698 (2002) 193

20. Elliptic flow as a function of centrality Non-flow considerable for central and peripheral events STAR Nucl. Phys. A698 (2002) 193

21. Calculating flow using multi particle correlations Assumption all correlations between particles due to flow Non flow correlation contribute order (1/N), problem if vn≈1/√N Non flow correlation contribute order (1/N3), problem if vn≈1/N¾ N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906

22. Integrated v2 from cumulants STAR, PRC 66,(2002) 034904

23. Non-flow estimate from pp At low-ptnon-flow estimate from pp 5-10% of observed v2 in AA STAR preliminary See Aihong’s talk

24. Yet another view on non-flow Fluctuation probably too large; estimate of maximum effect on v2

25. Comparing optical to MC Glauber

26. Eccentricity Fluctuations

27. Fluctuation and their effect on cumulant calculations

28. Fluctuation contribution to extracted v2 v2{2} at mid-central collisions 10% higher than real v2 v2{4} at mid-central collisions 10% lower than real v2

29. Conclusion • Comparable measurements of elliptic flow from PHENIX, PHOBOS and STAR • Elliptic flow well described by boosted thermal particle distributions • Flow is large; indicative of strong parton interactions at early stage of the collision • Up to pt = 6 GeV/c sizable elliptic flow • Elliptic flow measurement at low to intermediate pt is real correlation with the reaction plane • Fluctuation could be main contribution to non-flow; At mid-central collisions the maximum effect is 10%

30. Identified particle v2 at high-pt • See Huan’s talk • Double splitting of v2(pt) for the different particles • parton coalescence at intermediate pt? Voloshin QM2002 Preliminary