1. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page1 Anisotropic Flow. Part II Sergei A. Voloshin Wayne State University, Detroit, Michigan

2. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page2 Outline Part I. Physics 1. Introduction. Definitions. 2. Directed flow - Physics of the “wiggle” - Blast wave parameterization - Coalescence I. Directed flow of light nuclei. Resonances. 3. Elliptic flow - General properties. “Early times” - Low Density and “Hydro” Limits - Phase transition - Blast wave. “Mass splitting - Coalescence II. Constituent quarks. - Elliptic flow at high pt’s. 4. Anisotropies and asymmetries - Femtoscopy of anisotropic source - High pt, 2-particle correlations - Global polarization. Parity violation. 5. Can we measure it? - correlations induced by flow - “Non-flow”. Flow fluctuations Part II. Methods and Results 1. Non-flow estimates - From the “resolution plot” - Azimuthal correlations in pp and AA 2. Multiparticle correlations - 4-particle cumulants. Methods. - Non-flow and flow fluctuations - Mixed harmonics. 3-particle correlations. - Distributions in q-vector - Detector effects 3. Main results - Reaching the hydro limit - Mass splitting - Constituent quark scaling - Elliptic flow at high pt - v1 and higher harmonics - other 4. Conclusion

3. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page3 End of the ideal world: “Non-flow”, flow fluctuations, … “ Non-flow” – azimuthal correlations of any other origin except the correlation with respect to the reaction plane. It combines the possible contributions from resonance decay, inter and intra jet correlations, etc. An example: Flow   “non-flow” Effect of flow fluctuations Other possibilities fro flow fluctuations: fluctuation in the initial geometry, in multiplicity at the same geometry, etc. Not perfect azimuthal acceptance  not flat Event Plane distribution. “Flattening of the reaction plane”. Approximate and exact solutions to the problem. Each one by itself presents little problem, but taken at the same time, it is the major problem we fight during the last years.

4. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page4 Non-flow estimates

5. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page5 Non-Flow estimates from the reaction plane resolution plot STAR. PRL 86 (2001) 402 Non-flow level

6. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page6 Non-flow. Depends on centrality? Multiplicity M 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 Correlations induced by transverse radial expansion S.V. nucl-th/0312065 STAR nucl-ex/0409033

7. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page7 Azimuthal correlation in pp collisions Goals (from “flow” point of view): 1.Check if non-flow estimates/measurements reported for Au+Au are consistent with measurements in pp. (One could expect the difference of the order of factor of <~2. Examples: Extra particles in jets  non-flow contribution increases B-to-B jet suppression – non-flow goes down) 2.Use pp data to estimate non-flow effects in Au+Au in the regions where other methods do not work well (e.g. high p t region; Kaon and Lambda flow, etc. )

8. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page8 Scalar product method and pp vs. AA Notations: Flow in a particular p t /eta “bin” Average flow in the pt/eta region used to define RP (or “pool” of particles) Azimuthal correlations in pp ( ) Non-flow part in 2-part azimuthal correlation in AA Number of “independent NN collisions”, a la N part /2. Non-flow looks exactly the same in pp and AA  Results - directly “correctible”. Consider correlations of particles from some “bin” with all particles from a “pool”

9. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page9 pp vs. AA The plot above, showing the rise and fall of azimuthal correlations ( M ) can be explained only by flow: no any other known source of the azimuthal correlation is able to give such a dependence. The origin of such a dependence: ~ M *  STAR Preliminary Most peripheral 5% central 0 p t 7 GeV M<~10 M>~500

10. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page10 Final results: pp & 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. It does not mean that v 2 is zero! STAR: PRL 93(2004)252301 Analysis has to be continued: charge combination dependence, identified particles…

11. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page11 Many-particle correlations

12. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page12 flow*nflow + nflow*flow (1,3)(2,4)+(1,4)(2,3) Non-flow and multiparticle correlations p t weight “ON” 12/15/2000 Assuming

13. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page13 flow*nflow + nflow*flow (1,3)(2,4)+(1,4)(2,3) Non-flow and multiparticle correlations STAR Application: Generating functions (Borghini, Ding, Ollitrault) + many other ways

14. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page14 Non-flow or Fluctuations? Correct if v is constant in the event sample Should be used even in a case of  =0 Several reasons for v to fluctuate in a centrality bin: 1)Variation in impact parameter (taken out in STAR 130 GeV PRC flow paper) 2)Real flow fluctuations (due to fluctuations in initial conditions or in system evolution) Non-flow Flow fluctuations In this approximation, v is between v{4} and (v{2}+v{4})/2.

15. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page15 Getting v 2 (b) Procedure: - Assume some form for v 2 (b) - Use any event generator to relate multiplicity and impact parameter - calculate powers of v - compare to what is measured by v2{4} Note: the curves in the plot are NOT fit to the points how/where the points are shown

16. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page16 Fluctuation in eccentricity  v 2 {2} vs v 2 {4} x,y – coordinates of “wounded” nucleons v 2 ~   fluctuations in flow Calculations: R. Snellings and M. Miller

17. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page17 v 2 {4}/v 2 {2} : Compare to data R. Snellings The flow fluctuations calculated with participating nucleons is too strong compared to the data !

18. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page18 Mixed harmonics: how it works What to do when the reaction plane is known: … and when it is not exactly known: Similar for v 4 via Borghini, Dinh, Ollitrault PRC 66(2002)014905 Poskanzer, S.V. PRC 58 (1998)1671 3-particle correlation: Y X Main non-flow contribution left is due to resonance/jets that flow themselves The difference between x component and y component correlations:

19. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page19 q-distribution Two more: 1)q-distributions: 2)Q vector products Distribution in the magnitude of the flow vector Correlations due to flow Non-flow contribution Used in the very first E877 analysis

20. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page20 v 2 from q-distributions -- The results are very close to those from 4-particle correlation analysis. -- Difficult to trace the contribution of flow fluctuations. STAR, PRC 66 (2002) 034904

21. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page21 A few comments on some of the results

22. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page22 Anisotropic flow from AGS to RHIC QM’95 ( organized by Art! ): Y. Zhang (E877) – technique, first measurements at AGS (free of non-flow!) D. Miśkowiec (E877) – first attempt for HBT with respect to the reaction plane J.-Y. Ollitrault – drew attention to non-flow effects and how to deal with them M. Gyulassy (concluding remarks) : “The discovery of collective sidewards flow in Au+Au at the AGS is a major highlight of this year. … It is of fundamental importance because it provides a direct probe of the equation of state at extremely high densities….” E. Shuryak: “… probably the most direct signature of QGP plasma formation, observed at RHIC.” (nucl-th/0112042 ) U. Heinz: “… resulting in a well developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c” (hep-ph/0109006). STAR. PRL 86 (2001) 402 The highest citation index of any (?) experimental paper on heavy ion collisions

23. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page23 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. PHOBOS It is measured vs: - collision energy - transverse momentum - centrality - particle ID

24. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page24 Energy dependence PHENIX nucl-ex/0410003

25. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page25 Where we are – checking with “oldstuff” S.V. RHIC Winter Workshop, Berkeley, January 1999 http://www-rnc.lbl.gov/~nxu/oldstuff/workshop/rww99.html        ? Unexpected – constituent quark scaling

26. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page26 Quark Scaling

27. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page27 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; Levai, Ko; … -> Eremin, S.V.

28. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page28 Constituent quark scaling - Constituent quark scaling holds very well. Deviations are where expected. - Elliptic flow saturates at pt~ 1 GeV, just at constituent quark scale. An accident? Gas of free(?) constituent quarks – deconfinement ! STAR PRL 92(2004)052302

29. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page29 AuAu@62 GeV STAR Preliminary AuAu@62 GeV

30. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page30 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??

31. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page31 Comparison with Hydro

32. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page32 v 2 (p t ): Comparison with hydro Hydrodynamic model - describes the data rather well But should it? (non-flow, min-bias, etc.) STAR, PRL 87, 182301 (2001)

33. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page33 Recent preprint P. Houvinen, nucl-th/0505036

34. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page34 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.

35. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page35 Hydro vs LDL How LDL results would look like if calculated for constituent quark?

36. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page36 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

37. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page37 Integrated v 2 at different energies (0-40% central) We still have to analyze carefully the centrality dependence

38. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page38 Hydro limits Hydro: P.F. Kolb, et al Questions to address: - is it saturating? - add rapidity dependence? - what happens at SPS energies? Any ‘wiggle’? - uncertainty in the centrality definition - sqrt(s)=130 GeV data: 0.075 < pt < 2.0 GeV/c - sqrt(s)=200 GeV data: 0.15 < pt < 2.0; the data scaled down by factor of 1.06 to account for change in (raw) mean pt. - AGS and SPS – no low pt cut - STAR and SPS 160 – 4 th order cumulants

39. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page39 “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?

40. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page40 Charged particle v 2 at high-p t phenix preliminary nucl-ex/0305013 STAR: PRL 93(2004)252301 v 2 (p t ) has maximum at about 3 GeV/c Above 6 GeV we do not have a reliable answer (yet) what the real flow contribution is

41. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page41 But is it surprising?: v 2 stays the same? STAR SQM04 Charm flow (via electron measurements)

42. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page42 New possibilities Anisotropies and asymmetries 1.HBT with respect to the reaction plane 2.Non-identical particle correlations with respect to the reaction plane 3.High pt 2-particle correlation wrt reaction plane 4.Global polarization in AA 5.Parity violation

43. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page43 Hanbury Brown – Twiss interferometry of an anisotropic source Proposed: S.V. & W. Cleland, PRC 53 (1996) 896; PRC 54(1996) 3212 Further technique developments : U. Wiedemann, U. Heinz, M. Liza First attempt to measure : D. Miskowiec, E877, QM ’95 First and subsequent real measurements : M. Lisa et al., E895, STAR Let us measure the geometry of anisotropic source! x y Can we see the evolution?

44. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page44 T=100 MeV,  0  R=11.7 fm,  =2.2 fm/c  a  s 2  =0.037 Blast wave model : Same parameters fit R(  ) and v  (p T,m) Hanbury Brown – Twiss interferometry of an anisotropic source STAR PRL 93(2004)012301 STAR PRC 71(2005)044906

45. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page45 azHBT S.V. LBNL 1998 annual report # R20 http://ie.lbl.gov/nsd1999/rnc/RNC.htm RQMD v 2.3, AuAu @ RHIC In this picture at high energies /high p t, the relative difference between out-of-plane size and in-plane size only increases.

46. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page46 azHBT-2 IPES initial conditions, U. Heinz, P. Kolb PL B542 (2002) 216 Note “out-of-phase” R side modulations for k=0 case. Should we try very low k T at RHIC?

47. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page47 Do different particles freeze-out at the same place?

48. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page48 Non-identical 2-particle correlations S.V., R. Lednicky, S. Panitkin, Nu Xu, PRL 79 (1997) 4766

49. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page49 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 92(2004)032901 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 STAR, PRL 93 (2004) 252301

50. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page50 Parity, CP- violation, global polarization… D. Kharzeev, hep-ph/0406125 : Emission of positive (negative) pions could be asymmetric along the system angular momentum Liang, Wang, nucl-th:0410079. PRL S.V. nucl-th:0410089 Large orbital momentum of the system can be transformed into particle spin momentum  global polarization Observing parity (CP) violation with anisotropic flow techniques Kharzeev, Pisarski, Tytgat, PRL 81 (1998) 512 Kharzeev, Pisarski, PRD 61 (2000) 111901 S.V. PRC 62 (2000) 044901 S.V. PRC 70 (2004) 057901 Parity violation Global polarization “Oriented” DCC Asakawa, Minakata, Müller, nucl-th/0212070 Negative elliptic flow of neutral pions

51. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page51 SUMMARY It looks like the first 20 (?) year is just the very beginning…

52. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page52 “Perfect” flattening E877 PRC 56 (1997) 3254

53. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page53 Doing it exactly

54. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page54 Non-flow and mixed harmonics Compare to 5—6  10 -3 reported. -- Totally relies on non-flow estimates for v2. -- Higher order cumulants do not help All estimates are given for STAR acceptance !

55. S.A. Voloshin School of Collective Dynamics in High Energy Collisions, LBNL, May 19-27, 2005page55 pasi P. Houvinen, nucl-th/0505036