1. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page1 Anisotropic Flow and Phase transitions, …and a little bit on fluctuations/correlations Sergei Voloshin Wayne State University, Detroit Outline: - Anisotropic flow: where to look for a phase transition - v 1 (y) - directed flow “wiggle” - v 2 (p t ) – constituent quark number scaling - v 2 (p t ) – “mass splitting” and QGP - v 2 (energy,centrality) – approaching “hydro limit” - v 2 /  vs dN/dy/S, any “wiggle/step”? - Correlation functions and fluctuations. - Centrality dependence of and radial flow. - Conclusions

2. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page2 Directed flowElliptic flow Term “flow” does not mean necessarily “hydro” flow – used only to emphasize the collective behavior  multiparticle azimuthal correlation. Anisotropic flow Fourier decomposition of single particle inclusive spectra: X Z XZ – the reaction plane Picture: © UrQMD Anisotropic flow  correlations with respect to the reaction plane Note large orbital angular momen- tum in the system. - Parity violation - Orbital momentum  particle spin.

3. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page3 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

4. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page4 Third flow component as the QGP signal L.P. Csernai, D. Rohrich PRL 458 (1999) 454 “Wiggle is present only for the QGP EoS. This calculations have been done at 11 AGeV. Would the results change for RHIC?

5. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page5 Wiggle from anti-flow: development in time. J. Brachmann Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke, PRC 61, 024909 (2000)

6. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page6 Wiggle from uRQMD Marcus Bleicher, Horst Stocker PLB 526, (2002) 309-314 “Rich” dependence on the particle type: baryons, antibaryons, mesons

7. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page7 Anti-flow from shadowing Anti-flow is developing in more peripheral collisions

8. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page8 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” R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003 The wiggle is pronounced only at high energies Does the picture contradict FOPI results on different isotope collisions?

9. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page9 QM2002 Warning: Large systematic errors!

10. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page10 Laszlo’s slide from BNL Flow workshop ‘03 The slope of v1(eta) at eta=0 is indeed as in antiflow scenario, … but also the same as always for pions at lower energies

11. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page11 PHOBOS, v1(eta) Qualitatively the same picture from SPS energies to highest RHIC energy.

12. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page12 STAR: ZDC-SMD SMD is an 8 channel by 7 channel hodoscope that sits directly on the face of the 2nd ZDC module What about ALICE, CMS, do they have something like that?

13. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page13 v1(eta), v1(pt), AuAu@62 GeV,different centralities STAR preliminary Qualitatively the picture is very similar at different centralities

14. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page14 Comparison with models. Centrality dependence STAR preliminary - In order to prove the “wiggle” one needs identified particle measurements and look for the change of sign of the slope with energy/centrality. At 62 GeV the errorbars are too large, we hope to have it such results for 200 GeV data. Neither model describes v1(eta) close to midrapidty

15. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page15 Elliptic Flow. XZ-plane - the reaction plane X Y v 2 > 0, E877, PRL 73 (1994) 2532 Sensitive to “early” times. (Free streaming kills  )

16. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page16 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. In mid and more central collisions elliptic flow is rather well described by hydro model PHOBOS It is measured vs: - collision energy - transverse momentum - centrality - rapidity - particle ID

17. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page17 Integrated v 2 at different energies (0-40% central) We still have to analyze carefully the centrality dependence

18. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page18 Constituent quark model + coalescence Side-notes: a) more particles produced via coalescence rather than 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; Levai, Ko; … -> Eremin, S.V. R. Fries

19. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page19 Constiuent quark scaling: v 2 and R CP - Constituent quark scaling holds well. Deviations are where expected. - Elliptic flow saturates at pt~ 1 GeV, just at constituent quark scale. An accident? Gas of constituent quarks – deconfinement !? AuAu@62 GeV STAR Preliminary

20. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page20 AuAu@62 GeV STAR Preliminary PHENIX: const. quark scaling, v 2 saturates at RHIC energy

21. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page21 Are they thermalized? S. Pratt, S. Pal, nucl-th/0409038 Two pictures correspond to the same v 2 of quarks, but a)v 2 (B) = 3/2 v 2 (M) (no thermalization ?) b)v 2 (B) = v 2 (M) (freeze-out at constant phase space density) My conclusion: constituent quark scaling  - Deconfinement! - No thermalization (at least in this region of pt) (Freeze-out at constant density in the configuration space) The same mechanism at sqrt(s_NN) 200 and 62 GeV. If thermalized, disappear at LHC??

22. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page22 v 2 (p t ) at 200 GeV. “Mass splitting”. Mass dependence is rather well reproduced by hydrodynamical model calculations. Note dependence on the EoS. But qualitatively such a mass dependence will be present in any model, for example, in the constituent quark coalescence picture (heavier particle  larger difference in constituent quark momenta) Data: PHENIX, Nucl. Phys. A715, 599, 2003 Hydro: P. Huovinen, P. Kolb, U. Heinz, P. Ruuskanen, S.V., Phys. Lett. B503, 58, 2001;

23. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page23 v2(pt) @ 200 and 62 GeV 0 ~ 80 % star preliminary pion Y. Bai (STAR), DNP ‘04 PtPt min. bias 0 ~ 80% star preliminary STAR expects good identified particle v2 measurements up to relatively high pt. Need detailed/tuned hydro calculations for different centralities and identified particles.

24. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page24 Centrality dependence. Hydro and Low Density limits Hydro: P.F. Kolb, et al v 2 /  5 10 b (fm) SV & A. Poskanzer, PLB 474 (2000) 27 hydro LDL (pts are RQMD v2.4) Hydro: v 2 ~  Ollitrault, PRD 46 (1992) 229 Low Density Limit: v 2 ~  dN/dy / A Heiselberg & Levy, PRC C59 (1999) 2716 RHIC 160 GeV/A SPS SPS 40 GeV/A b (fm) Suppressed scale!

25. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page25 v 2 /  and phase transitions Centrality dependence: Sorge, PRL 82 2048 (’99), Heiselberg & Levy, PRC 59 2716 (’99) Dependence on the particle density in the transverse plane: 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

26. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page26 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? - what happens at SPS energies? Any ‘wiggle’?

27. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page27 “Cold” deconfinement, color percolation? Percolation point by H. Satz, QM2002 CERN SPS energies b ~ 4 fm RHIC: b ~ 7 fm There is a need for the “next generation” of this plot: better estimates of epsilon, adding more data (in particular 62 GeV) It is a real pity that NA49 measurements have so large systematic uncertainty. Need detector with better azimuthal acceptance (could be just a simple extra detector used to determine the RP). FT RHIC?

28. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page28 But is it surprising?: v 2 stays the same? STAR SQM04 Charm flow (via electron measurements)

29. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page29 Correlations/fluctuations

30. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page30 2-particle correlation functions Production via N c clusters [e.g. independent NN collisions] Relation to fluctuations “Fluctuations” are determined by the “average“ value of the correlation function over momentum region under study. “Inclusive” ISR data. Filled circles – sqrt(s) = 63 GeV RHIC: PHOBOS? Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) “Probability” to find a “correlated” pair

31. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page31 fluctuations: observables and observables. What are the main requirements for a good observable? -- be sensitive to the physics under study -- be defined at the “theoretical level”, be detector/experiment independent -- have clear physical meaning -- not to be limited in scope, provide new venues for further study Possibilities: - test scaling with N ch, N part, N bin, etc. -Particles “1” and “2” could be of different type (e.g. same/opposite charge), - taken from different rapidity/azimuthal angle regions (e.g. “same-side”, |y 1 -y 2 |>1 correlations as mostly “free” from jet contribution).

32. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page32 Multiplicity fluctuations “Charge” fluctuations ! - Free from “volume” fluctuations  - Fails at small  - - “used” multiplicity, subject to cuts and acceptance Particle ratios:

33. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page33 Comparison to PHENIX, F pt (slide from G. Westfall (STAR), QM’04) 200 GeV Au+Au STAR with PHENIX Cuts |  | < 0.35  = 2x90  0.2 < p t < 2 GeV 200 GeV Au+Au STAR Cuts |  | < 1.0  = 360  0.1 < p t < 2 GeV

34. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page34 STAR Preliminary Elliptic flow contribution to Shengli Huang (STAR) USTC RHIC Workshop, Hefei, China, Oct. 2004 y x In-plane Out-of-plane Could be better to plot / ^2

35. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page35 correlations: elongation in  ISR data. Filled circles – sqrt(s) = 63 GeV “Inclusive” R (  ) ~ 1 -  |  |  (Y) ~ 1 - 4/3  Y, where Y = (  ) max /2 max Blue dotted lines assume the same . Note difference in slopes (red vs blue) – broadening of R (  ) with centrality All data on are STAR preliminary, taken from talks of G. Westwall (STAR) at QM2004 and Nuclear Dynamics WSs ‘04 and ‘05 A way to do it better  study directly as function of y 1 and y 2

36. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page36 R cc (0)  0.66 : centrality dependence Production via N c clusters (N c ~N part /2) [e.g. independent NN collisions] Data: G. Westfall (STAR), QM2004 At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected. In a superposition of two independent collisions, the ratio of the probability that in a randomly chosen pair both particles are from the same collision to the probability that two particles are from different collisions is about 1.66

37. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page37 “Elementary” NN-collision. Correlation functions. Correlations are due to local charge(s) conservation, resonances, due to fluctuations in number of produced strings, e.g. number of qq-collisions. x y rapidity R cc (0)  0.66 Distribution of “correlated” pairs: Distribution of “associated” particles (2) per “trigger” particle (1) “Probability” to find a “correlated” pair ISR At midrapidity, the probability to find a particle is about 60% larger if one particle has been already detected.

38. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page38 Radial flow  2- particle correlations All particles produced in the same NN-collision (qq-string) experience the transverse radial “push” that is (a) in the same direction (leads to correlations in phi) (b) the same in magnitude (  correlations in p t )  Position-momentum correlations caused by transverse expansion “brings” totally new mechanism for momentum correlations, not present in NN-collisions x y rapidity pp collision AA collision  -Long range rapidity correlations (“bump”- narrow in phi and wide in rapidity, charge independent) -Stronger 2-particle pt correlation in narrow phi bins -Narrowing of the charge balance function ( -- increase in m t  decrease in rapidity separation) [same as in S. Pratt et al, in “late hadronization scenario”] - Charge correlations in phi. Azimuthal Balance function Everything evolving with centrality (radial flow)

39. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page39 Transverse radial expansion Blast wave parameterization (Schnedermann, Sollfrank, Heinz, PRC 48, 2462 (1993), d 3 n/d 3 p ~ e -E/T ) of the source at freeze-out: Parameters: T-temperature, velocity profile  t  r n STAR Collaboration, PRL 92, 112301 (2004) AA collision Note: uniform source density at r < R has been assumed y rapidity x n=1

40. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page40 Azimuthal correlations Figures are shown for particles from the same NN collision. Dilution factor to be applied! No momentum conservation effects has been included. Those would be important for the charge independent first harmonic correlations. First and second harmonics of the distribution on the left ! - the large values of transverse flow, > 0.25, would contradict “non-flow” estimates in elliptic flow measurements n=1, T=110 MeV

41. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page41  x  correlations - Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction. For those, one needs 2d correlations (rapidity X azimuth) Shown below – hand drawn sketch.   PeripheralCentral

42. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page42     Extracting Near-Side Jet Yields d+Au, 40-100% Au+Au, 0-5% STAR preliminary 3 < p T (trig) < 6 GeV 2 < p T (assoc) < p T (trig) In Au+Au, jet-like correlation sits on top of an additional, approximately flat correlation in  D. Magestro (STAR) – Hard Probes 2004

43. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page43 Brief comparison to data: centrality dependence Possible reasons for discrepancy: - diffusion, thermalization time - spatial source profile (not uniform density in transverse plane, e.g. cylinder shell) n=1 n=0.5

44. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page44 correlation summary 1.Transverse radial flow leads to strong space-momentum correlation. In combination with space correlations between particles created in the same NN collision, it leads to characteristic two (and many) particle rapidity, transverse momentum, and azimuthal correlations. 2.This phenomenon provides a natural (at present, qualitative) explanation of the centrality dependence of mean p t pseudorapidity/azimuthal angle correlations. It can be further used to study the details of the system equilibration/thermalization and evolution (e.g. thermalization time, velocity profile, etc.) 1. Avoid using ratios (n+/n-, K+/K0,…), use to get rid of “volume” fluctuations and be free from problems related to low multiplicities. 2. If use normalized variance – correct for the efficiency.

45. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page45 EXTRA SLIDES

46. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page46 Rapidity correlations How to disentangle “initial” correlations at the parton production stage and obtained due to the transverse expansion? - Charge dependent and charge independent correlations. - Correlation of conserved charges (Balance Functions). In this case the correlations existed already at the production moment would be modified (narrowed) by radial flow. - Charge independent correlations: particles at large rapidities, initially uncorrelated, become correlated, as all of them are pushed by radial flow in the same direction. Charge Balance function As increases due to the transverse radial flow, the balance function gets narrower. For the BW parameters used above, indeed increases for about 15-20%, but the centrality dependence is somewhat different from what is observed in the narrowing of the Balance Function.

47. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page47 Initial and freeze-out configurations Final initial Uncertainty: particles are at the same position at the moment of production, but the blast wave parameterization is done at freeze-out Smearing would depend on the - thermalization time (which is supposedly small) - diffusion during the system evolution before freeze-out - non-zero “expansion velocity” in pp Should we take it as a possibility to study all the above effects?

48. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page48 AA collision. “Single jet tomography”. The plot on the right shows particle azimuthal distribution (integrated over all pt’s) with respect to the boost direction. In order to compare with data it should be also convoluted with jet azimuthal distribution relative to radial direction. In this picture, the transverse momentum of the (same side, large  ) associated particles would be a measure of the space position the hard scattering occurred AA collision

49. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page49 Sensitivity to the velocity profile Results for n=0.5 and n=2 are shown Mean p t is almost insensitive to the actual velocity profile. The correlations are. In general, mean p t is sensitive to the first moment of the respective transverse rapidity distribution while the two particle correlation are measuring the second moment.

50. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page50 Parity violation study via 3-particle correlations a > 0  preferential emission along the angular momentum The sign can vary event by event, a~Q/N , where Q is the topological charge, |Q|=1,2,…  at dN/dy~100, |a|~1%. And using only one particle instead of the event flow vector projections onto reaction plane Projections on the direction of angular momentum note that for a rapidity region symmetric with respect to the midrapidity v 1 =0 hep-ph/0406311 All effects non sensitive to the RP cancel out! Possible systematics: clusters that flow Looking for the effect of D. Kharzeev, hep-ph/0406125

51. S.A. Voloshin 2 nd Int. Workshop on the Critical Point and Onset of Deconfinement, Bergen, 2005page51 Ebye and inclusive approaches Most of the present measurements are done this way Would be better, easier to analyze theoretically. (! Numerically both are very close)