1. Anisotropic Flow; from the sQGP at RHIC towards the (s?)(w?)QGP at the LHC Raimond Snellings QGP Meeting, Variable Energy Cyclotron Centre, February 5, Kolkata, India

2. 7/5/20052 Outline Heavy Ion collisions and the Quark Gluon Plasma Probing the QGP: The azimuthal dependence of particle production versus the reaction plane Measuring particle production versus the reaction plane The EOS of hot and dense QCD matter magnitude of elliptic flow (v 2 ) centrality dependence of elliptic flow v 2 (mass,p t ), sensitivity to freeze-out and the QCD EoS What have we learned so far? The magic of mid-rapidity and highest RHIC energy elliptic flow versus energy and rapidity Other harmonics System size dependence and energy dependence What can we learn at the LHC with ALICE

3. 7/5/20053 QCD at extreme conditions Heavy-ion collisions provide experimental access to the properties of QCD matter at extreme temperature and density (the Equation of State at the QGP phase transition and in the QGP phase) Better understand the evolution of our universe Deconfinement The building blocks of QCD, quarks and gluons, become quasi free Approximate chiral symmetry restoration The origin of our mass Lattice QCD predicts a phase transition to a quark gluon plasma at energy densities of about 1 GeV/fm 3 and at a temperature of about 170 MeV The quark gluon plasma is a state of matter expected to have existed in the early universe about 1 microsecond after the Big Bang

4. 7/5/20054 Phases of QCD matter: The Quark Gluon Plasma Theory view of phases in QCD matter  B → 0 and high temperatures accessible in ultra relativistic heavy-ion collisions Krishna Rajagopal and Frank Wilczek: Handbook of QCD

5. 7/5/20055 Interpreting Heavy Ion Collisions QGP properties are in principle calculable from the QCD Lagrangian using lattice QCD Lattice QCD calculations are not yet advanced enough to form a solid basis for a quantitative comparison of experiment with theory → try to learn as much as possible from comparison to baseline data A reference measurement is provided by elementary collisions p+p and p+A At the LHC p+A certainly not before 2010 Or by collision geometry Centrality dependence Azimuthal dependence

6. 7/5/20056 Non-central A-A collisions Non central collisions break the azimuthal symmetry! Observables, like collective motion and medium modification of jets, become azimuthally dependent.

7. 7/5/20057 Jet Quenching: the initial color density Thick plasma (Baier et al.): Thin plasma (Gyulassy et al.): Radiated gluons decohere due to multiple interactions with the medium This energy loss depends on the traversed path length and gluon density at the early phase

8. 7/5/20058 v 2 (p t ) for high p t particles (self normalizing tomography of dense matter) M. Gyulassy, I. Vitev and X.N. Wang PRL 86 (2001) 2537 R.S, A.M. Poskanzer, S.A. Voloshin, STAR note, arXiv:nucl-ex/9904003 http://www.lbl.gov/nsd/annual/rbf/n sd1998/rnc/RNC.htm Event Anisotropy as a Probe of Jet Quenching R.S and X.-N. Wang

9. 7/5/20059 The QCD Equation of State: pressure and  nergy density Large increase of degrees of freedom at T c observed in quick change in energy density and pressure Pressure gradient, dp/d  generates collective flow At the phase transition  changes faster than p. Here dp/d  has its minimum, the so called softest point F. Karsch, E. Laermann and A. Peikert, Phys. Lett. B 478 (2000) 447

10. 7/5/200510 Collective motion: the velocity of sound Velocity of sound C s = (dp/d  ) 1/2 different magnitude for system of quarks and gluons (1/3) and a hadronic system (0.2). Minimum in velocity of sound during phase transition so called softest point Buildup of collective flow depends on the magnitude of the velocity of sound and the relative time spend in various phases P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084

11. 7/5/200511 Manifestations of Collective Flow (radial and anisotropic) x y x y z x Only type of transverse flow in central collision (b=0) is radial flow Integrates pressure history over complete expansion phase Elliptic flow (v 2 ), hexadecupole flow (v 4 ), v 6, … caused by anisotropic initial overlap region (b > 0) More weight towards early stage of expansion. Directed flow (v 1 ), sensitive to earliest collision stage (b > 0) pre-equilibrium at forward rapidity, at midrapidity perhaps different origin

12. 7/5/200512 The magic of elliptic flow: self quenching, direct measure of multiple-interactions P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084 The driving force of elliptic flow dominates at “early” times 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 p+p) Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow

13. 7/5/200513 t(fm/c) Main contribution to elliptic flow develops “early” in the collision P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084 Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45 dimensional arguments: time proportional to size of the system, depends on centrality (“early” in peripheral, “late” in central collisions) early depends on how long the system lives (timescales are of same order!) Hydro v2v2 v2v2 t(fm/c) Zhang’s parton cascade

14. 7/5/200514 Measuring particle production versus the reaction plane

15. 7/5/200515 Particle production versus the reaction plane: anisotropic flow Phenomenological description of collective effects Natural in hydrodynamic language, however when we talk about flow we do not necessary imply (ideal) hydrodynamic behavior Flow in cascade models: depends on constituent cross sections and densities, partonic and/or hadronic (low-density mode) gave reasonable (better than ideal hydro) description at lower energies Anisotropic flow ≡ correlation with the reaction plane Non-flow ≡ contribution to v n from correlations between particles not due to their correlation with the reaction plane (HBT, resonances, jets, etc)

16. 7/5/200516 Anisotropic flow is calculated using azimuthal 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) 054906 Can be conveniently calculated using generating functions, extended to v n {∞} using Lee-Yang zeros, reliable v n >1/N

17. 7/5/200517 Methods comparison (data) Clearly needed to compare results from different methods Does not tell you what the underlying physics is which causes this difference Complete models should be able to reproduce all these correlations! Like to have different checks e.g. correlating signal between detectors with much larger rapidity gap (like ZDC-SMD) For now: if physics conclusion depends on better than 10-20% agreement one has to be very careful! Aihong Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020, STAR PRL93 (2004) 252301; arXiv:nucl-ex/0409033

18. 7/5/200518 non-flow or fluctuations? ≠ n Measuring the cumulants of different order provides constraints on both fluctuations and non-flow.(does not take into account PHOBOS  part ) M. Miller and RS, arXiv:nucl-ex/0312008

19. 7/5/200519 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/0312008

20. 7/5/200520 Non-flow or fluctuations? N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906 Non-flow should give a constant g 2 which is not compatible with the data N is number of clusters, could go like multiplicity, number of wounded nucleons, number of binary collisions, etc M. Miller and RS, arXiv:nucl-ex/0312008

21. 7/5/200521 Non-flow or fluctuations UrQMD: Includes fluctuations and various non-flow contributions. In these calculations v 2 {4} reproduces true v 2. Non flow mechanisms ala Voloshin’s radial flow?

22. 7/5/200522 Methods to determine v n Non of the methods are perfect Presently still unclear how much is non-flow and how much is fluctuations (in Cu+Cu, fluctuations and non- flow could be very important) Important to have various methods to determine the reaction plane (and therefore flow) Important to have various regions in phase space to determine the reaction plane A reasonably safe estimate is that the real flow is in between (v 2 {2}+v 2 {4})/2 and v 2 {4} Getting the reaction plane from v 1 is an ideal cross check (ZDC-SMD)

23. 7/5/200523 Integrated elliptic flow

24. 7/5/200524 Excitation Function Smooth increase as function of center of mass energy At low energies negative elliptic flow due to shadowing of the spectator matter, “squeeze out”

25. 7/5/200525 just 20k events STAR Phys. Rev. Lett. 86, 402–407 (2001); Nucl. Phys. A698 (2002) 193 Charged particle elliptic flow at low p t ; one of the first results from RHIC First time quantitative agreement with hydrodynamics -> evidence of early pressure and approaching early thermalization For peripheral collisions hydrodynamics breaks down Charged particle elliptic flow (RHIC): It’s in the magnitude!

26. 7/5/200526 Charged particle elliptic flow: It’s in the magnitude! For mid-central collisions magnitude of the integrated charged particle elliptic flow well described by ideal hydrodynamics Magnitude of integrated charged particle elliptic flow is a factor two bigger than expected in hadronic cascade calculations Evidence for strongly interacting pre-hadronic phase! v 2 {4} 130 GeV Zhixu Liu STAR Phys. Rev. Lett. 86, 402–407 (2001)

27. 7/5/200527 Charged particle elliptic flow: Transverse momentum dependence v 2 (p t ) at top RHIC energies for charged particles disagrees with low density limit (LDL) and is consistent with hydrodynamics up to about 2 GeV/c At lower energies the p t dependence of v 2 is also not well described by LDL P.F. Kolb et al., Phys.Lett.B500 232-240 (2001) 0012137

28. 7/5/200528 v 2 (p t ) and particle mass (the fine structure): some details On what freeze-out variables does it depend (simplification)? The average velocity difference in and out of plane (due to  p) But also The average freeze-out temperature The average transverse flow The average spatial eccentricity

29. 7/5/200529 Hydro Motivated Fit (blast-wave) STAR Phys. Rev. Lett. 87, 182301 (2001) More recent and extended approach in: F. Retiere and M.A. Lisa Phys.Rev.C70:044907,2004

30. 7/5/200530 The effect of freeze-out temperature and radial flow on v 2 Light particle v 2 (p t ) very sensitive to temperature Heavier particles v 2 (p t ) more sensitive to transverse flow T = 100 MeV,  2 =0.05 F. Retiere and M.A. Lisa, Phys.Rev.C70:044907,2004  0 =0.9,  2 =0.05

31. 7/5/200531 The effect of the azimuthal asymmetric flow velocity and shape Larger value of the difference in collective velocity in and out of the reaction plane leads to larger slope of v 2 (p t ) above ~ of the particle Larger spatial anisotropy leads to larger v 2 with little mass dependence (transverse flow boosts more particles in the reaction plane) F. Retiere and M.A. Lisa, Phys.Rev.C70:044907,2004 T = 100 MeV,  0 =0.9

32. 7/5/200532 Blast wave gives convenient summery of the data Even these 4 parameters are a simplification The interplay of these can give quite complicated behavior and interpreting the meaning is not straight forward In a true dynamical model these parameters are connected v 2 (mass,p t ) reflects complete system evolution: the flow contributions from QGP phase, phase transition and hadron gas Ideal hydro, ideal hydro + cascade, parton cascade + coalescence, ideal + viscous, viscous + ideal + viscous, etc

33. 7/5/200533 STAR QM2001 Mass dependence Identified particle elliptic flow at low p t Mass dependence in accordance with collective flow. QGP equation of state (phase transition) provides best description Hydro calculation: P. Huovinen et. al.

34. 7/5/200534 Mass dependence pions to Cascade follow the mass dependence at low-p t Ideal hydro provides a reasonable description (common velocity and common freeze-out!)

35. 7/5/200535 Mass dependence At larger transverse momenta the v2(pt) start to deviate from hydro The mass dependence breaks down, in fact the various particle species cross

36. 7/5/200536 Charged particle elliptic flow at higher p t Exceeds extreme jet quenching (surface emission) break down from ideal hydro but it needs an extra contribution E. Shuryak: nucl-th/0112042

37. 7/5/200537 Identified particle elliptic flow at higher p t one of the surprises at RHIC D. Molnar and S. Voloshin, Phys.Rev.Lett. 91 (2003) 092301 Baryon/meson scaling at intermediate transverse momenta: fits in coalescence picture, mass effect opposite to expectations from hydrodynamics Explains the larger than expected elliptic flow at intermediate p t Why does this simple picture work so well? Elliptic flow of particles unaffected by the hadronic phase (lucky windows at intermediate p t )? What about space momentum correlations? Could this mechanism be an alternative for ideal hydro behavior?

38. 7/5/200538 Charged particle elliptic flow at higher p t v 2 measured in region where coalescence contribution is expected to diminish However, due to non-flow uncertainties no detailed conclusions can be drawn so far STAR PRL93 (2004) 252301; arXiv:nucl-ex/0409033

39. 7/5/200539 Experimental summary of the first 3 years and the BNL statement RHIC Scientists Serve Up “Perfect” Liquid New state of matter more remarkable than predicted -- raising many new questions April 18, 2005

40. 7/5/200540 Main arguments for the ideal fluid- like behavior Large elliptic flow, strongly interacting system which approaches ideal hydrodynamics Inconsistent with conventional hadronic approaches A more complete description of ideal hydro + hadron cascade shows that at top RHIC energies v 2 is dominated by the ideal hydro contribution (for real detailed comparison hadron cascade is needed) Magnitude of mass scaling of elliptic flow (the fine structure) is consistent with Hydrodynamics Particles exhibit common flow velocity (if strange and multistrange particles deviate, it must be in the details of the fine structure) Hydro is constrained at RHIC Initial conditions in hydro consistent with densities obtained from jet quenching and estimates from CGC EoS used in hydro consistent with lattice QCD calculations (more on that next) Viscous correction quickly destroy agreement with data (D. Teany)

41. 7/5/200541 In the press

42. 7/5/200542 AdS/CFT November, 2005 Scientific American “The Illusion of Gravity” J. Maldacena A test of this prediction comes from the Relativistic Heavy Ion Collider (RHIC) at BrookhavenNational Laboratory, which has been colliding gold nuclei at very high energies. A preliminary analysis of these experiments indicates the collisions are creating a fluid with very low viscosity. Even though Son and his co-workers studied a simplified version of chromodynamics, they seem to have come up with a property that is shared by the real world. Does this mean that RHIC is creating small five-dimensional black holes? It is really too early to tell, both experimentally and theoretically.

43. 7/5/200543 Dependence on the EOS! Test the effect of four different EoS; qp is lattice inspired, Q has first order phase transition, H is hadron gas with no phase transition and T a smooth parameterization between hadron and QGP phase Remember C 2 s = dp/d  closely related to acceleration   p/(  +p) Pasi Huovinen, arXiv:nucl-th/ 0505036

44. 7/5/200544 Dependence on the EOS! Integrated charged particle flow not so sensitive to the EoS (due to spectra constraint in ideal hydro?) Pasi Huovinen, arXiv:nucl-th/ 0505036

45. 7/5/200545 Dependence on the EOS! EoS Q and EoS T (both have significant softening) do provide the best description of the magnitude of the mass scaling in v 2 (p t ) The lattice inspired EoS (EoS qp) in ideal hydro does as poorly as a hadron gas EoS! Pasi Huovinen, arXiv:nucl-th/ 0505036 Detailed agreement between ideal hydro and measured v 2 (mass,p t ) an accident? (Hirano and Gyulassy arXiv:nucl-th/0506049)

46. 7/5/200546 Charged particle elliptic flow: The centrality dependence Different centrality dependence between hydro (proportional to  and peaks around b=12 fm) and low density limit (peaks around b=8 fm) Data peaks around b ≈10 fm (in between LDL and hydrodynamics) Slightly shifting to larger b for 200 GeV compared to 62 However not corrected for non-flow yet which (can) shift it to smaller b pions: 0.2 < p t <0.7 Adapted from S.A. Voloshin and A.M. Poskanzer, Phys.Lett.B474 27-32 (2000) 9906075 STAR preliminary Yuting Bai

47. 7/5/200547 v 2 /  versus multiplicity density STAR Phys. Rev. C 66, 034904 (2002) v 2 scales monotonic with the particle density from AGS to RHIC The “physics” does not change from AGS to RHIC !?!? v 2 reaches the hydro limit for the more central collisions at the highest RHIC energies What will happen at the LHC ?

48. 7/5/200548 QGP QGP QGP Wanna see this? Fine-tune the “hadronic” focus! focus: hadron corona LDL or hadronic corona From T. Hirano

49. 7/5/200549 Beam energy dependence energy dependence only described by hybrid models (or phenomenological scaling) non-ideal component more important at lower energies (and at forward rapidities). What will happen at the LHC? D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).

50. 7/5/200550 3D-Hydro Incomplete thermalization away from mid-rapidity Connected to energy dependence? Hirano: Nucl Phys A715 821 824 2003; Heinz and Kolb: J. Phys. G Nucl. Part. Phys. 30 S1229

51. 7/5/200551 Energy and  dependence of v 2 PHOBOS Phys. Rev. Lett. 94, 122303 (2005) no boost invariance and monotonic dependence on energy

52. 7/5/200552 What about the eccentricity(  )?

53. 7/5/200553 Top RHIC energies at dip in v 2 Hydro prediction for lower energies v 2 increases? the radial flow increases monotonically with beam energy (pion multiplicity at fixed impact parameter), is the slope of v 2 (p t ) expected to increase for ideal hydro? Where are the 62 GeV calculations? Adapted from P.F. Kolb and U. Heinz, in Quark Gluon Plasma, nucl-th/0305084 Energy dependence of v 2 (p t ) Is the slope of v 2 (p t ) more sensitive to the energy dependence?

54. 7/5/200554 v 2 / energy dependence Slope of v 2 (p t ) seems to saturate How significant is it, does it signal softening of the EOS? Need quantitative model calculations K. Paech, H. Stocker, A. Dumitru: Phys. Rev. C 68, 044907 (2003) ; PHENIX arXiv:nucl-ex/0411040

55. 7/5/200555 Energy dependence of v 2 (p t ) For charged particles PHENIX observes similar v 2 (p t ) at 62 and 200 GeV while the difference with 17 GeV (CERES) is much bigger PHENIX What is the reason for this similar behavior? Are the individual contributions from the different particles also so similar (naïve expectations are somewhat larger flow and different relative contribution from the various (mass) particles as function of p t )? PHENIX arXiv:nucl-ex/0411040

56. 7/5/200556 Lower energies: identified particles Identified particles are to first order very similar at 62 and 200 GeV ReCo works also well at intermediate transverse momenta at 62 GeV Can it be an alternative for ideal hydro: LDL plus coalescence? STAR preliminary Xin Dong STAR preliminary Yuting Bai

57. 7/5/200557 What about higher harmonics? Higher harmonics are natural but are expect to be small v 4 - a small, but sensitive observable for heavy ion collisions (Peter Kolb, PRC 68, 031902) v 4 - magnitude sensitive to ideal hydro behavior (Borghini and Ollitrault, arXiv:nucl-th/0506045) Ideal hydro v 4 /v 2 2 = 0.5 -0.04 -0.02 0.02 0.04 0

58. 7/5/200558 pion v 4 at 62 and 200 GeV Measured relative to the 2 nd order event plane v 4 for pions is positive and similar at 62 and 200 GeV over large range in p t STAR preliminary Yuting Bai

59. 7/5/200559 v 4 scaling with v 2 2 Even in detail at low-p t v 4 is within uncertainties the same at 62 and 200 GeV and the scaling with v 2 2 (the dashed lines) holds for both energies Ratio approximately unity which according to Borghini and Ollitrault is inconsistent with ideal hydrodynamics See no obvious change as function of collision energy Lines v 2 2 STAR preliminary Yuting Bai

60. 7/5/200560 Smaller systems Too early do draw conclusions, large differences between methods in Cu+Cu

61. 7/5/200561 Summary Elliptic flow is a very powerful observable Its magnitude in agreement with prediction from ideal hydrodynamics and ideal hydro + hadron cascade Mass dependence of elliptic flow in agreement with common collective velocity and favors soft effective EOS The basis of the ideal fluid statement The break down of hydro behavior at more peripheral collisions higher transverse momenta and away from midrapidity can be understood and was qualitatively predicted in hydro+hadron cascade calculations (Teany and Shuryak) However, the observed monotonic behavior also naturally expected in scaling with dN/dy. Would like to see at least some change in slope of energy dependence v 2 /  (slope of v 2 (p t ) perhaps more sensitive?) What about v 4 ? Still a lot to do and understand (both at RHIC and at the LHC)

62. 7/5/200562 The LHC accelerator

63. 7/5/200563 ALICE Set-up HMPID Muon Arm TRD PHOS PMD ITS TOF TPC Size: 16 x 26 m Weight: 10,000 tons

64. 7/5/200564 The perfect fluid at RHIC, the wQGP at the LHC? Less flow at higher energies? Remember the predictions for RHIC!

65. 7/5/200565 Past experiences, no guarantee for the future?

66. 7/5/200566 Elliptic flow at LHC energies from ideal hydrodynamics Whatever the outcome will be it is a day 1 measurement at the LHC with very likely similar impact as at RHIC From Heinz, Kolb, Sollfrank

67. 7/5/200567 The End

68. 7/5/200568 Velocity of sound from Lattice Minimum in velocity of sound C s = (dp/d  ) 1/2 Buildup of collective flow depends on the magnitude of the velocity of sound and the relative time spend in various phases Need sensitivity to (integrals of)  p/   during different parts of the system evolution! F. Karsch and E. Laermann, arXiv:hep-lat/0305025

69. 7/5/200569 In what direction is RHIC flowing? Spectra and v 2 of multistrange particles and phi meson promise an additional handle on the pre-hadronic dynamics What is the accuracy needed? What is the guidance from theory calculations? The radial and anisotropic flow of charm Partial charm quark thermalization constraint for thermalization light quarks? Increase the energy density: U+U collisions? What do we expect at higher energies?

70. 7/5/200570 Mean Free Path & Viscosity For ultra-relativistic particles, the shear viscosity is Ideal hydro:  0  shear viscosity  0 Transport cross section

71. 7/5/200571 Jet quenching: it’s a final state phenomena! Strong suppression (5x) in the inclusive hadron yields and the away- side azimuthal correlation while no suppression in d+Au: jet-quenching clearly final state phenomenon

72. 7/5/200572 High-p t suppression: big effect! D. d’Enterria High-p t hadron yields are suppressed by a factor 5!

73. 7/5/200573 The initial color density is large! Medium induced radiative energy loss (jet quenching) is the only currently known physical mechanism that can consistently explain the high-p t suppression Within such models, initial gluon densities of about dn g /dy~1000 are obtained. This corresponds to an initial energy density  ~15 GeV/fm 3 (more than 50X cold nuclear matter gluon density) Consistent with simple Bjorken estimates from dE T /d  Consistent with input initial conditions in hydrodynamic models Does the system strongly re-interact and does it approach thermalization?

74. 7/5/200574 ALICE

75. 7/5/200575 v 4 scaling with v 2 2 Calculations from Huovinen with ideal hydro with freeze-out conditions matching the inclusive spectra, do however match the v 4 measurements (EoS dependent) Pasi Huovinen, arXiv:nucl-th/ 0505036

76. 7/5/200576 The “perfect” liquid at RHIC Nature Vol. 430 page 499 (2004) Sometimes theorist do get their feet wet and experimentally test fluid behavior When physicist talk about a perfect liquid, they don’t mean the best glass of champagne they ever tasted. The word “perfect” refers to the liquid’s viscosity