1. Anisotropic Flow Raimond Snellings

2. Raimond Snellings; Trento 20042 What have we learned from elliptic flow so far? According to: –U. Heinz: Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/0109006). –E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl- th/0112042). –L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/0202025). –M. Gyulassy: The most powerful probe of the QGP equation of state: the mass dependence of v 2 ; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/0403032).

3. Raimond Snellings; Trento 20043 Outline Elliptic flow: –v 2 at low p t, the dependence on particle mass and its relation to freeze-out parameters in a hydro motivated picture –Some uncertainties related to the measurement –What are the changes from SPS to RHIC energies?

4. Raimond Snellings; Trento 20044 Elliptic flow of the bulk 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 y x coordinate space pypy pxpx Momentum space

5. Raimond Snellings; Trento 20045 Time evolution Elliptic Flow reduces spatial anisotropy -> self quenching SCIENCE Vol: 298 2179 (2002) Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz

6. Raimond Snellings; Trento 20046 Main contribution to elliptic flow develops early in the collision Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45

7. Raimond Snellings; Trento 20047 Non-central heavy-ion collisions: coordinate system

8. Raimond Snellings; Trento 20048 Hydrodynamic limit STAR PHOBOS Hydrodynamic limit STAR PHOBOS Compilation and Figure from M. Kaneta Integrated Elliptic Flow First time in Heavy-Ion Collisions a system created which at low p t is in quantitative agreement with ideal hydrodynamic model predictions for v 2 up to mid-central collisions PHOBOS: Phys. Rev. Lett. 89, 222301 (2002) STAR: Phys. Rev. Lett. 86, 402 (2001) PHENIX: Phys. Rev. Lett. 89, 212301 (2002) RQMD

9. Raimond Snellings; Trento 20049 Identified particle v 2 Typical p t dependence for different masses 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  p Hydro: P. Huovinen, P. Kolb, U. Heinz STAR

10. Raimond Snellings; Trento 200410 Hadron Cascade UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep- ph/0006147 Magnitude off in v 2 and different scale in p t

11. Raimond Snellings; Trento 200411 v 2 (p t,mass) All particles reasonably described at low-p t with common set of parameters PHENIX (squares) and STAR agree well STAR, PHENIX preliminary

12. Raimond Snellings; Trento 200412 Everything flows? p T [GeV/c] M. Kaneta (PHENIX) QM2004 J. Castillo (STAR) QM2004 What about charm?

13. Raimond Snellings; Trento 200413 Reaction plane determination Anisotropic flow ≡ azimuthal correlation with the reaction plane Experimentally the reaction plane  r is unknown Can introduce “non-flow” contributions

14. Raimond Snellings; Trento 200414 Determining the reaction plane

15. Raimond Snellings; Trento 200415 Event plane resolution Event plane resolution  N * v 2 2 Most non flow contributions v 2  1/  N Kovchegov and Tuchin: N = N wounded 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

16. Raimond Snellings; Trento 200416 Elliptic flow as a function of centrality STAR Nucl. Phys. A698 (2002) 193 Non-flow considerable for central and peripheral events

17. Raimond Snellings; Trento 200417 Calculating flow using multi particle correlations Assumption all correlations between particles due to flow Non-flow correlation contribute order (1/N), problem if v n ≈1/√N Non-flow correlation contribute order (1/N 3 ), problem if v n ≈1/N ¾ N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906

18. Raimond Snellings; Trento 200418 Higher moments ≠ n

19. Raimond Snellings; Trento 200419 Integrated v 2 from cumulants A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020 About 20% reduction from v 2 {2} to v 2 {4} v 2 {4} ≈ v 2 {6}

20. Raimond Snellings; Trento 200420 The possible fluctuation contribution “standard” v 2 {2} overestimates v 2 by 10%, higher order cumulant underestimate v 2 by 10% at intermediate centralities M. Miller and RS, arXiv:nucl-ex/0312008

21. Raimond Snellings; Trento 200421 Integrated v 2 from cumulants A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020 About 20% reduction from v 2 {2} to v 2 {4} v 2 {4} ≈ v 2 {6}

22. Raimond Snellings; Trento 200422 How does it compare to data? M. Miller and RS, arXiv:nucl-ex/0312008

23. Raimond Snellings; Trento 200423 Non-flow or fluctuations? M. Miller and RS, arXiv:nucl-ex/0312008 NA49: Phys.Rev. C68 (2003) 034903 N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906

24. Raimond Snellings; Trento 200424 Uncertainties Non-flow and fluctuations expected in general to both contribute At mid-central collisions (20-60%) the estimated effect is about 10%. IMO best estimate of the true flow are in between (v 2 {2}+v 2 {4})/2 and v 2 {4}

25. Raimond Snellings; Trento 200425 Elliptic flow at lower energies P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C62 054909 (2000). Increase of about 50% in v2 from top SPS to top RHIC energy

26. Raimond Snellings; Trento 200426 Hydrodynamics + RQMD D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).

27. Raimond Snellings; Trento 200427 Energy dependence NA49 Phys.Rev. C68 (2003) 034903 At low energies pions, at RHIC charged hadrons. This makes a difference, this figure approximates the excitation plot of h -

28. Raimond Snellings; Trento 200428 v 2 (p t ) SPS-RHIC Integrated v 2 depends on slope and pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles ≈ 500 MeV/c NA49: Phys. Rev. C68 (2003) 034903; CERES: Phys. Rev. Lett. 92 (2004) 032301

29. Raimond Snellings; Trento 200429 Similar or very different? arXiv:nucl-ex/0305001

30. Raimond Snellings; Trento 200430 Similar or very different?? Note: only statistical errors plotted

31. Raimond Snellings; Trento 200431 Similar or very different?

32. Raimond Snellings; Trento 200432 Summary Consistent measurements of elliptic flow at RHIC from PHENIX, PHOBOS and STAR Elliptic flow for all measured particles at low-p t well described by boosted thermal particle distributions Smooth increase in elliptic flow from SPS to RHIC. Detailed measurements of identified particle v 2 (p t ) by the RHIC experiments (or perhaps SPS data not presented yet) will provide a clearer picture At intermediate centralities (20-60%) I estimate not more than 10% uncertainty in the integrated elliptic flow values At RHIC the large elliptic flow is not described by hadronic models; strong (partonic) interactions at early stage of the collision are needed From comparisons with ideal hydro calculations early thermalization deduced (is this the only possibility? what is the freedom in EOS? What about HBT?) D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).

33. Raimond Snellings; Trento 200433 Backup

34. Raimond Snellings; Trento 200434 Elliptic flow; excitation function NA49 Phys.Rev. C68 (2003) 034903 NA49 STAR

35. Raimond Snellings; Trento 200435 Hydro + Jet Quenching? X.-N. Wang: nucl-th/0305010 T. Hirano and Y. Nara: nucl-th/0307015 Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-p t

36. Raimond Snellings; Trento 200436 Flow (radial, directed and elliptic) x y x y z x Only type of transverse flow in central collision (b=0) is transverse flow. Integrates pressure history over complete expansion phase Elliptic flow, caused by anisotropic initial overlap region (b > 0). More weight towards early stage of expansion. Directed flow, sensitive to earliest collision stage (pre-equilibrium, b > 0)

37. Raimond Snellings; Trento 200437 v 1 predictions (QGP invoked) J. Brachmann et al., Phys. Rev. C. 61 024909 (2000) L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454

38. Raimond Snellings; Trento 200438 v 1 predictions (more general, QGP interpretation not necessary) R.S., H. Sorge, S.A. Voloshin, F.Q. Wang, N. Xu: Phys. Rev. Lett 84 2803 (2000) M. Bleicher, H. Stocker: Phys. Lett. B 526 (2002) 309 (UrQMD)

39. Raimond Snellings; Trento 200439 Directed flow at the SPS (NA49) NA49: Phys.Rev. C68 (2003) 034903

40. Raimond Snellings; Trento 200440 First measurement of v 1 at RHIC A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin Confirms v 2 is in-plane at RHIC Suggestive of limiting fragmentation picture Consistent with theory predictions The data with current statistics shows no sign of a wiggle (also does not exclude the magnitude of the wiggle as predicted

41. Raimond Snellings; Trento 200441 Is there boost invariance? PHOBOS v2(  ) Preliminary v 2 200 Final v 2 130 200 130 average over all centrality (N part ~200) PHOBOS: Phys. Rev. Lett. 89, 222301 (2002)

42. Raimond Snellings; Trento 200442 Elliptic flow at higher p t, extracted using multi-particle correlations Significant v 2 up to ~7 GeV/c in p t as expected from jet quenching. However at intermediate p t the magnitude is unexpectedly large STAR Preliminary v 2 {2} v 2 {RP} v 2 {4} A. Tang (STAR) QM 2004

43. Raimond Snellings; Trento 200443 Early freeze-out in a blast wave approach Low-p t measurements and comparison to full dynamical calculations important for drawing a conclusion !!!! STAR, PHENIX preliminary