1. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page1 Sergei A. Voloshin Wayne State University, Detroit, Michigan Collective phenomena in non-central nuclear collision

2. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page2 Major RHIC discoveries “The physical picture emerging from the four (RHIC) experiments is consistent and surprising. The quarks and gluons indeed break out of confinement and behave collectively, if only fleetingly. But this hot mélange acts like a liquid, not the ideal gas theorists had anticipated.” M. Riordan, W. Zajc, Sci. Am., May 2006, 34-41. Three major RHIC discoveries (my view): 1. Large elliptic flow 2. Jet quenching 3. Constituent quark scaling Note the importance of item #3 observed in anisotropic flow “sector” (the observation in spectra would not constitute that strongly “partonic flow” - deconfinement !). RHIC I snow in the second pahse - quantitative understanding of sQGP- and I discuss some recent results in this respect Outline 1. v 2 /ε: - Advances in hydro calculations - …including viscous effects. - Understanding initial conditions - and fluctuations in those 2. Non-flow and flow fluctuations. Flow fluctuations in the Gaussian model and beyond 3. Anisotropic initial conditions  v 2, v 1, a 1 and more. 4. Future: RHIC beam energy scan, LHC 5. Conclusions Directed flow Elliptic flow

3. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page3 Elliptic flow and sQGP (“s”=strongly coupled) STAR. PRL 86 (2001) 402 v 2 /ε indicates the respond of the system, how well the initial spatial eccentricity is “transformed” into momentum anisotropy

4. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page4 - How well we measure v 2 ? (Non-flow, Flow fluctuations, participant plane vs reaction plane, etc.) v 2 /ε plot (respond of the system): recent developments - Did we use “right” initial conditions in hydro calculations? (do we compare apples to apples when comparing data to the “hydro limits”?) - What is the role of viscosity? - Have we missed important effects in our description/calculations? There are many components in this plot. We are now questioning each and any of them. Is there a saturation? Findings: - Viscosity leads to decrease of flow  (v 2 /ε) theor down ~30% - Initial eccentricity is likely higher than thought  (v 2 /ε) theor up ~<50% - “proper” selection of parameters in hydro  (v 2 /ε) theor up ~20% - “Correcting for flow fluctuations  (v 2 /ε) exp down <~ 20% - Initial flow field  (v 2 /ε) theor up ~?

5. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page5 First look at viscous effects. Eccentricity in Color Glass Condensate model. “late viscosity” was simulated by hydro+cascade MC. The details depend in particular on transverse coordinate dependence of the saturation scale, if entropy or energy density is used as a weight,… Lappi, Venugopalan Phys.Rev.C74:054905,2006

6. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page6 Viscous hydro calculations: real progress

7. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page7 Viscous hydro calculations vs data  η /s is about factor of 2 larger compared to the conjectured low limit of 1/(4π), It is still the most “perfect” liquid!

8. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page8 How far are we from the “hydro limit”? note that there is a difference of a factor of “2” in the definitions of S - Even central Au+Au collisions are about 30-50% away from ideal hydro limit. - η /s is about factor of 2 -- 4 larger compared to the conjectured low limit of 1/(4π), Note: assumed constant speed of sound - no phase transitions, change in initial conditions with energy, 2d, boost invariance, etc..

9. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page9 Gaussian model of eccentricity fluctuations  v 2 {4} measures “true” elliptic flow (wrt reaction plane) – exactly what is needed for comparison with theory! Model assumes Gaussian form for the distributions in ε x and ε y, (which is a very good approximation of MC Glauber calculations). In this model it is not possible to separate flow fluctuations and non-flow effects (this can be traced to the fact that the Gaussian distribution has all cumulants higher than rank 2 equal to zero)

10. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page10 Differential flow, v 2 {4} and “standard” ε was used in this plot! The maximum flow is reached at higher transverse momenta in more central collisions  indicates higher degree of “thermalization” in more central collisions

11. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page11 Modification of the initial conditions Initial flow field is non-isotropic. It might be an important effect to include into calculations! Revival of interest to the picture of rotating system (Dremin, Kharzeev, …) Contribution to the in-plane expansion due to initial (longitudinal) velocity gradient It must also lead to directed flow! Indeed… rapidity p x, v 1 x rapidity pxpx x

12. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page12 Directed flow G. Wang (STAR), QM2006 Not quantitatively explained by any model (even close)! Error-bars at the level of < 10 -3 ! AuAu and CuCu are very similar at the same centrality! (Magenta curves are polynomial fits to guide the eye) High accuracy of these measurements achieved by - using STAR ZDC-SMD (“spectator neutrons”) - 3 –particle correlations (mixed harmonics) 3 particle correlations measure the difference in correlations projected into the reaction plane and out-of-plane directions making use of strong elliptic flow to define the plane..

13. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page13 Probe for the strong parity violations The largest uncertainty from “flowing” clusters( e.g. decay of flowing resonances)

14. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page14 Nearest future: RHIC Beam energy scan Low energy scan: Search for the phase transition 1. Collapse of directed flow 2. Non-monotonic behavior of v2/eps, and/or scaling violation (may also reflect change in the initial conditions (e.g. participant Glauber  CGC) U=U Collisions With upgrades we will have 1. Higher pt reach 2. Better PID, and more

15. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page15 LHC “Naive” extrapolations lead to elliptic flow values at LHC up to 50% larger than at RHIC. Hirano, et al., QM2006 - Predictions are made. - Collaborations ready Looking forward for the first collisions

16. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page16 Very briefly, constituent quark number scaling Constituent quark number scaling strongly suggests that the matter is in deconfined state. But there are questions.. - mt-m scaling: Is it “accidental” or it says something? - Is it consistent with thermalization? - where and how it is violated? (we need dynamical models!)

17. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page17 Conclusions 1. Significant progress in understanding of - the role of viscosity - initial conditions - flow fluctuations 2. New ideas for the anisotropic flow are being developed, such as - role of non-zero vorticity (system rotation) 3. Directed flow still remains under explored. 3. Constiuent quark number scaling needs full understanding. Azimuthal correlations analyses of non-central collisions established to be one of the most informative direction in HIC studies ( + Global polarization, parity violation studies, etc.) Bright and exciting future at RHIC and LHC!

18. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page18 Backup slides

19. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page19 Net baryon density flow antiflow Hydro: “antiflow”, “third flow component” Brachmann, Soff, Dumitru, Stocker, Maruhn, Greiner Bravina, Rischke, PRC 61 (2000) 024909 rapidity v1v1 Csernai, Rohrich, PLB 458 (1999) 454. Magas, Csernai, Strottman, hep-ph/0010307 R. Snellings, H. Sorge, S.V., F. Wang, Nu Xu, PRL 84 (2000) 2803 M. Bleicher, H. Stocker, PRB 526 (2002) 309 R. Snellings, A. Poskanzer, S.V., nucl-ex/9904003 RQMD v2.4

20. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page20 Higher cumulant results, data and UrQMD calculations v2{2}=v2{4}=v2{6}=v2{LYZ}=v2{ZDC-SMD) and it looks like we now know why. What was puzzling before in this calculations, were why no effect of eccentricity fluctuations had been seen.

21. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page21 Ideal Hydro  Viscous hydro Ideal hydro, if tuned to spectra, over predicts elliptic flow! Including viscosity might improve agreement with data.

22. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page22 v 2 { FTPC } (p t ), 20-60% centrality There still indications of non-flow contribution in v 2 {FTPC}, especially at high transverse momenta. The green points show the results “AA-pp” [G.Wang (STAR), QM2005] AuAu 200 GeV CuCu 200 GeV Non-flow contribution in v 2 {2}, relatively small in AuAu @200 GeV, increases with p t

23. S.A. Voloshin PANIC 2008, Eilat, Israel, November 9-14, 2008. Anisotropic flow:…page23 CuCu 200 GeV, v 2 { FTPC } (p t ) STAR Preliminary Indicates strong non-flow contribution in v 2 {2} (measured within Main TPC). Non-flow might be still present at high p t in v 2 {FTPC}