Anisotropic Flow Raimond Snellings

Raimond Snellings; Trento 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/ ). –E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl- th/ ). –L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/ ). –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/ ).

Raimond Snellings; Trento 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?

Raimond Snellings; Trento 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

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

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

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

Raimond Snellings; Trento 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, (2002) STAR: Phys. Rev. Lett. 86, 402 (2001) PHENIX: Phys. Rev. Lett. 89, (2002) RQMD

Raimond Snellings; Trento 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

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

Raimond Snellings; Trento 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

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

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

Raimond Snellings; Trento Determining the reaction plane

Raimond Snellings; Trento 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

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

Raimond Snellings; Trento 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)

Raimond Snellings; Trento Higher moments ≠ n

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

Raimond Snellings; Trento 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/

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

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

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

Raimond Snellings; Trento 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}

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

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

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

Raimond Snellings; Trento 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) ; CERES: Phys. Rev. Lett. 92 (2004)

Raimond Snellings; Trento Similar or very different? arXiv:nucl-ex/

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

Raimond Snellings; Trento Similar or very different?

Raimond Snellings; Trento 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/ ; Phys. Rev. Lett 86, 4783 (2001).

Raimond Snellings; Trento Backup

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

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

Raimond Snellings; Trento 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)

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

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

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

Raimond Snellings; Trento 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

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

Raimond Snellings; Trento 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

Raimond Snellings; Trento 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