1. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page1 RHI Collisions. Dense Matter. Anisotropic Flow Sergei Voloshin Wayne State University Outline: - Anisotropic flow as a tool for early dynamics study - Most important results of recent years: - Constituent quark scaling - mass splitting of v 2 (p t ) - Approaching “hydro limit” - First results on directed flow and higher harmonics - Conclusions and what to expect from exp. in the next couple years How much the nature of hadronization affects anisotropic flow ? Do we have constituent quark plasma?

2. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page2 Directed flowElliptic flow Term “flow” does not mean necessarily “hydro” flow – used only to emphasize the collective behavior  multiparticle azimuthal correlation. Anisotropic flow. Definitions. Fourier decomposition of single particle inclusive spectra: X Z XZ – the reaction plane Picture: © UrQMD Anisotropic flow  correlations with respect to the reaction plane S.V., Y.Zhang, 1994

3. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page3 Elliptic Flow – a probe for early time physics. t (fm/c) Zhang, Gyulassy, Ko, PL B455 (1999) 45 Elliptic flow XZ-plane - the reaction plane X Y Sensitive to the physics of constituent interactions (needed to convert space to momentum anisotropy) at early times (free-streaming kills the initial space anisotropy) The characteristic time scale of 2-4 fm is similar in any model: parton cascade, hydro, etc. v 2 > 0, E877, PRL 73 (1994) 2532

4. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page4 Elliptic flow as function of … - Integrated values of v 2 noticeably increase with energy - The slope of v2(pt) increase slowly  Most of the increase in integrated v 2 comes from the increase in mean p t. Popular view: In mid and more central collisions elliptic flow is well described by hydro model, and not by microscopic transport models PHOBOS It is measured vs: - collision energy - transverse momentum - centrality - particle ID

5. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page5 MPC (D. Molnar and M. Gyulassy) AMPT+”string melting” (Zi-Wei Lin, C.M.Ko) v2v2 HIJING x 80 HIJING x 35 HIJING x 13 HIJING x 1 hydro, sBC Elastic scattering, Baseline (HIJING) parameters:  gg = 3 mb,  tr = 1 mb; 1 gluon  1 charged particle; dN glue /dy=210.  opacity =  tr dN/dy =210 mb Constituent quark plasma:  tr up 2 - 3 (?) times, dN/dy up > 2 times,  Could be close to the data… “ String melting”: a) # of quarks in the system = # of quarks in the hadrons b) “quark” formation time

6. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page6 Constituent quark model + coalescence Side-notes: a) more particles produced via coalescence vs parton fragmentation  larger mean p t … b)  higher baryon/meson ratio c)  lower multiplicity per “participant” coalescence fragmentation Low p t quarks High p t quarks Taking into account that in coalescence and in fragmentation, there could be a region in quark pt where only few quarks coalesce, but give hadrons in the hadron pt region where most hadrons are produced via coalescence. In the low pt region density is large and most quarks coalesce: N hadron ~ N quark In the high pt region fragmentation eventually wins: Only in the intermediate region (rare processes) coalescence can be described by :  S.V., QM2002 D. Molnar, S.V., PRL 2003 -> D. Molnar, QM2004, in progress -> Bass, Fries, Mueller. Nonaka; Hwa; Levai, Ko; … -> Eremin, S.V.

7. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page7 dN ch /dy vs. number of participants Open symbols: our calculation of N part The ratio N ch /N q-part slightly decreases with centrality ! S. Eremin, S.V., PRC 67, 064905( 2003) Scaled by number of quark participants Scaled by number of nucleon participants. The dependence usually explained by a combination of ‘soft’ and ‘hard’ physics

8. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page8 Constiuent quark scaling: v 2 and R CP - Constituent quark scaling holds very well. Deviations are where expected. - Elliptic flow saturates at pt ~ 1 GeV, just at constituent quark scale. An accident?

9. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page9 v 2 (p t ) dependence on mass. Blast wave model. v 1 (p t ) - S.V., PRC 55 (1997) 1630 v 2 (p t ) - Houvinen, Kolb, Heinz, Ruuskanen, S.V., PLB 503 (2001) 58 v 2 (p t ) - STAR Collaboration, PRL 87 (2001) 182301 Elementary source density - Parameters: T – temperature  0 - radial expansion rapidity  2 - amplitude of azimuthal variation in expansion rapidity STAR T (MeV) 135  20100  24 0.0 0.04  0.01 S2S2 00 aa 0.52  0.020.54  0.03 0.09  0.02 0.04  0.01 dashed solid - model fits data well - shape (s2 parameter) agrees with the interferometry measurements

10. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page10 v 2 (p t ) at 200 GeV. Comparison to hydro. Mass dependence is well reproduced by hydrodynamical model calculations, but can it also be accounted for in the constituent quark coalescence picture? (heavier particle  larger difference in constituent quark momenta) Data: PHENIX, Nucl. Phys. A715, 599 (2003) Hydro: P. Huovinen et al., Phys. Lett. B503, 58 (2001); Houvinen, Heinz, Kolb Mass splitting depends on EoS! Caveats: - centrality bins are very wide - Initial conditions are chosen independently for spectra and v2 descriptions

11. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page11 Heinz, Kolb, Sollfrank Hydro limits RHIC 160 GeV/A SPS SPS 40 GeV/A b (fm) Suppressed scale! Hydro: P.F. Kolb, et al v 2 /  Hydro: v 2 ~  Ollitrault, PRD 46 (1992) 229 Low Density Limit: v 2 ~  dN/dy / S Heiselberg & Levy, PRC C59 (1999) 2716 Questions to address: - is it saturating? - rapidity dependence? (next slide) - what happens at SPS energies? Any ‘wiggle’?

12. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page12 PHOBOS: rapidity dependence (nucl-ex/0406021) PRL 91, 052303 (2003) The detailed study of the rapidity dependence is still to be made, but it looks like v 2 (  ) follows very closely dN/d . Low Density Limit? Difficulty:  (  ) Steinberg, nucl-ex/0105013 (QM01)

13. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page13 v 2 /  and phase transitions Original ideas: Sorge, PRL 82 2048 (’99), Heiselberg & Levy, PRC 59 2716 (’99) S.V. & A. Poskanzer, PLB 474 (2000) 27 “Cold” deconfinement? Uncertainties: Hydro limits: slightly depend on initial conditions Data: no systematic errors, shaded area –uncertainty in centrality determinations. Curves: “hand made” E877 NA49

14. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page14 “Cold” deconfinement, color percolation? Percolation point by H. Satz CERN SPS energies b ~ 4 fm RHIC: b ~ 7 fm Could it be constituent quark deconfinement ?

15. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page15 Charged particle v 2 at high-p t Above 6 – 8 GeV we do not have a reliable answer (yet) for the magnitude of the elliptic flow phenix preliminary nucl-ex/0305013

16. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page16 Elliptic flow at intermediate pt (jet quenching ?) STAR, Au+Au, 200 GeV Hard shell Hard sphere Woods-Saxon Hard shell == box density profile (+) extreme quenching E. Shuryak, nucl-th/0112042 Hard sphere == -”- (+) realistic quenching Woods-Saxon == WS density profile (+) realistic quenching

17. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page17 Directed flow at RHIC: (Limiting fragmentation, etc.) STAR Preliminary A. Tang, HQ2004 rapidity v1v1 Looking for the ‘wiggle’: Directed flow is most sensitive to the initial conditions z x Radial flow  > 0 rapidity p x, v 1 R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803 x rapidity pxpx x Baryon stopping “wiggle”

18. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page18 v 4, v 6 @ 200 GeV 1.4 v 2 2 STAR, PRL 92, 062301 (2004) P. Kolb, hydro Detailed comparison of the event shape: not really described by any model

19. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page19 SUMMARY OBSERVATION: - Anisotropies are strong at RHIC - The magnitude of elliptic flow is close to hydro predictions (for rather central collisions) - The mass splitting in v2(pt) finds natural explanation in hydro model. The magnitude of the splitting requires QGP EoS. - In the intermediate pt region the constituent quark number scaling is observed. - No model describes all the details… QUESTIONS: - How well hydro models describe both, spectra and v 2, simultaneously? - How much ‘coalescence enhancement’ is reflected in ‘hydro limits’? - ‘Mass splitting’ at low pt – is the hydro explanation unique? - Constituent quark plasma picture – is it supported by theory / lattice QCD? What is the relation to color percolation? Do we have ’cold deconfinement’? WHAT TO EXPECT: - Elliptic flow of open charm. Does c-quark flow? - Elliptic flow of resonances. Check regeneration in the hadronic phase vs direct production - Elliptic flow up to 10-12 GeV with good accuracy. Check jet quenching mechanism. - Directed flow of identified particle. Baryon stopping, tilted source. - Two particle correlation wrt Reaction Plane. Jets, tilted source - Anisotropic flow in lighter systems (Cu+Cu?). Low Density Limit?

20. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page20 2-particle correlations wrt RP x – azimuthal angle, transverse momentum, rapidity, etc. J. Bielcikova, P. Wurm, K. Filimonov S. Esumi, S.V., PRC, 2003 “a” == “trigger particle” CERES, PRL, 2003 Selection of one (or both) of particles in- or out- of the reaction plane “distorts” the RP determination Approach: - “remove” flow contribution - parameterize the shape of what is left - study RP orientation dependence of the parameters

21. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page21 Azimuthal correlations from pp to AuAu pp (non-flow) AuAu (flow + non-flow) In VERY peripheral collisions, azimuthal correlation in AuAu are dominated by non-flow. At high p t in central collisions, azimuthal correlation in AuAu could be dominated by nonflow.

22. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page22 “Wiggle”, Pb+Pb, E lab =40 and 158 GeV Preliminary 158 GeV/A Note different scale for 40 and 158 GeV! The “wiggle” is there! v 1 < 0

23. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page23 Centrality dependence. Hydro + RQMD. LH8  latent heat = 0.8 GeV/fm^3 Pt slope parameters are about 20% larger in hydro compared to data 200 400 600 800 dN ch /dy Teaney, Lauret, Shuryak nucl-th/0110037 - v 2 increases with dN/dy - Centrality dependence – close to data

24. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page24 CERES/NA45 0-12.5% 12.5-23.5% >23.5% 24-30% Preliminary STAR Lines: horizontal – v 2 =0.1 vertical - p t =1 GeV/c Talks: NA49 – A. Wetzler NA45 – J. Slivova STAR- K. Filimonov PHENIX – S. Esumi PHOBOS – S. Manly 30-80% 10-30% 0-10% v 2 (p T ), low transverse momentum 0-55% 1.For midcentral collisions, v 2 (p t ) is quite similar between SPS and RHIC 2.For “central” collisions NA49 results are lower than STAR

25. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page25 Directed flow “wiggle” in cascade models z x Radial flow  > 0 rapidity p x, v 1 R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803 x rapidity pxpx x Baryon stopping “wiggle” UrQMD: Bleicher, Stocker, PRB 526 (2002) 309 R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003 RQMD v2.4 Should be better pronounced at higher energies

26. S.A. Voloshin International Symposium on Multiparticle Dynamics, Sonoma, CA, July 2004page26 Hydro: “antiflow”, “third flow component” Net baryon density Csernai, Rohrich, PLB 458 (1999) 454. Magas, Csernai, Strottman, hep-ph/0010307 Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke, PRC 61 (2000) 024909 - Strongest at the softest point ? - The same for pions and protons ? rapidity v1v1 flow antiflow