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Anisotropic Flow

Anisotropic Flow. Raimond Snellings. 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).

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Anisotropic Flow

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  1. Anisotropic Flow Raimond Snellings

  2. 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 v2; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/0403032). Raimond Snellings; Trento 2004

  3. Outline • Elliptic flow: • v2 at lowpt, 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? Raimond Snellings; Trento 2004

  4. y coordinate space x Momentum space py px 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 Raimond Snellings; Trento 2004

  5. Time evolution SCIENCE Vol: 298 2179 (2002) Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz • Elliptic Flow reduces spatial anisotropy -> self quenching Raimond Snellings; Trento 2004

  6. Main contribution to elliptic flow develops early in the collision Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45 Raimond Snellings; Trento 2004

  7. Non-central heavy-ion collisions: coordinate system Raimond Snellings; Trento 2004

  8. Hydrodynamic limit STAR PHOBOS Compilation and Figure from M. Kaneta Integrated Elliptic Flow PHOBOS: Phys. Rev. Lett. 89, 222301 (2002) PHENIX: Phys. Rev. Lett. 89, 212301 (2002) STAR: Phys. Rev. Lett. 86, 402 (2001) RQMD First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with ideal hydrodynamic model predictions for v2 up to mid-central collisions Raimond Snellings; Trento 2004

  9. Hydro: P. Huovinen, P. Kolb, U. Heinz Fluid cells expand with collective velocity v, different mass particles get different Dp Identified particle v2 • Typical pt dependence for different masses • Heavy particles more sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS STAR Raimond Snellings; Trento 2004

  10. Hadron Cascade Magnitude off in v2 and different scale in pt UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147 Raimond Snellings; Trento 2004

  11. v2(pt,mass) • All particles reasonably described at low-pt with common set of parameters • PHENIX (squares) and STAR agree well STAR, PHENIX preliminary Raimond Snellings; Trento 2004

  12. Everything flows? J. Castillo (STAR) QM2004 What about charm? M. Kaneta (PHENIX) QM2004 Raimond Snellings; Trento 2004 pT [GeV/c]

  13. Reaction plane determination • Anisotropic flow ≡ azimuthal correlation with the reaction plane • Experimentally the reaction plane Yr is unknown • Can introduce “non-flow” contributions Raimond Snellings; Trento 2004

  14. Determining the reaction plane Raimond Snellings; Trento 2004

  15. 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 Raimond Snellings; Trento 2004 STAR, PRL 86, (2001) 402, Nucl. Phys. A698 (2002) 193

  16. Elliptic flow as a function of centrality Non-flow considerable for central and peripheral events STAR Nucl. Phys. A698 (2002) 193 Raimond Snellings; Trento 2004

  17. 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 Raimond Snellings; Trento 2004

  18. Higher moments <v2n> ≠ <v2>n Raimond Snellings; Trento 2004

  19. Integrated v2 from cumulants About 20% reduction from v2{2} to v2{4} v2{4} ≈ v2{6} A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020 Raimond Snellings; Trento 2004

  20. The possible fluctuation contribution “standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities M. Miller and RS, arXiv:nucl-ex/0312008 Raimond Snellings; Trento 2004

  21. Integrated v2 from cumulants About 20% reduction from v2{2} to v2{4} v2{4} ≈ v2{6} A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020 Raimond Snellings; Trento 2004

  22. How does it compare to data? M. Miller and RS, arXiv:nucl-ex/0312008 Raimond Snellings; Trento 2004

  23. Non-flow or fluctuations? N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906 M. Miller and RS, arXiv:nucl-ex/0312008 NA49: Phys.Rev. C68 (2003) 034903 Raimond Snellings; Trento 2004

  24. 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 (v2{2}+v2{4})/2 and v2{4} Raimond Snellings; Trento 2004

  25. Elliptic flow at lower energies • Increase of about 50% in v2 from top SPS to top RHIC energy P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C62 054909 (2000). Raimond Snellings; Trento 2004

  26. Hydrodynamics + RQMD D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001). Raimond Snellings; Trento 2004

  27. NA49 Phys.Rev. C68 (2003) 034903 Energy dependence At low energies pions, at RHIC charged hadrons. This makes a difference, this figure approximates the excitation plot of h- Raimond Snellings; Trento 2004

  28. v2(pt) SPS-RHIC • Integrated v2 depends on slope and <pt> • <pt> pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles <pt> ≈ 500 MeV/c NA49: Phys. Rev. C68 (2003) 034903; CERES: Phys. Rev. Lett. 92 (2004) 032301 Raimond Snellings; Trento 2004

  29. Similar or very different? arXiv:nucl-ex/0305001 Raimond Snellings; Trento 2004

  30. Similar or very different?? • Note: only statistical errors plotted Raimond Snellings; Trento 2004

  31. Similar or very different? Raimond Snellings; Trento 2004

  32. Summary • Consistent measurements of elliptic flow at RHIC from PHENIX, PHOBOS and STAR • Elliptic flow for all measured particles at low-pt well described by boosted thermal particle distributions • Smooth increase in elliptic flow from SPS to RHIC. Detailed measurements of identified particle v2(pt) 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). Raimond Snellings; Trento 2004

  33. Backup Raimond Snellings; Trento 2004

  34. NA49 Phys.Rev. C68 (2003) 034903 STAR NA49 Elliptic flow; excitation function Raimond Snellings; Trento 2004

  35. Hydro + Jet Quenching? T. Hirano and Y. Nara: nucl-th/0307015 X.-N. Wang: nucl-th/0305010 Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-pt Raimond Snellings; Trento 2004

  36. y x y x x z Flow (radial, directed and elliptic) • 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) Raimond Snellings; Trento 2004

  37. v1 predictions (QGP invoked) L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454 J. Brachmann et al., Phys. Rev. C. 61 024909 (2000) Raimond Snellings; Trento 2004

  38. v1 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) Raimond Snellings; Trento 2004

  39. Directed flow at the SPS (NA49) NA49: Phys.Rev. C68 (2003) 034903 Raimond Snellings; Trento 2004

  40. Confirms v2 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 First measurement of v1 at RHIC A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin Raimond Snellings; Trento 2004

  41. Preliminaryv2200 Final v2130 200 130 Is there boost invariance?PHOBOS v2(h) PHOBOS: Phys. Rev. Lett. 89, 222301 (2002) average over all centrality (Npart ~200) Raimond Snellings; Trento 2004

  42. v2{2} v2{RP} v2{4} STAR Preliminary Elliptic flow at higher pt, extracted using multi-particle correlations Significant v2 up to ~7 GeV/c in pt as expected from jet quenching. However at intermediate pt the magnitude is unexpectedly large A. Tang (STAR) QM 2004 Raimond Snellings; Trento 2004

  43. Early freeze-out in a blast wave approach STAR, PHENIX preliminary • Low-pt measurements and comparison to full dynamical calculations important for drawing a conclusion !!!! Raimond Snellings; Trento 2004

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