1. R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna, Russia, July 14-26, 2008 Nuclear Chemistry Group SUNY Stony Brook, USA Elliptic Flow measurements at RHIC

2. R. Lacey, SUNY Stony Brook 2 Phase diagram (QCD) and RHIC How one can probe this new state of matter (QGP)?

3. R. Lacey, SUNY Stony Brook 3 One want to see a probe (phenomena) which is  Exist only in Heavy-Ion Collisions (HIC)  Provides reliable estimates of pressure & pressure gradients  Can address questions related to thermalization  Gives insides on the transverse dynamics of the medium  Provides access to the properties of the medium – EOS, viscosity, etc  Well calibrated : measured at Ganil (MSU), SIS, AGS, SPS energies Elliptic Flow in Heavy-Ion Collisions

4. R. Lacey, SUNY Stony Brook 4 Arkadij Taranenko Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna, Russia, July 14-26, 2008 Nuclear Chemistry Group SUNY Stony Brook, USA Elliptic Flow measurements from RHIC to SIS

5. R. Lacey, SUNY Stony Brook 5 “Squeeze-Out” - First Elliptic flow signal in HIC Reaction Plane +/- 90deg v2 < 0 mid-rapidity x y ψRψR φ=Φ-ΨRφ=Φ-ΨR Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990) Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989) Reaction plane

6. R. Lacey, SUNY Stony Brook 6 +/- 90deg v2 < 0 mid-rapidity Cheuk-Yin WONG, Physics Letters, 88B, p 39 (1979) Sergei Voloshin, Y. Zhang, Z. Phys. C70,(1996), 665 v1 < 0 +/- 180deg Directed flow Elliptic flow Fourier decomposition of single particle (semi) inclusive spectra: x y ψRψR φ=Φ-ΨRφ=Φ-ΨR KAOS

7. R. Lacey, SUNY Stony Brook 7 Small Elliptic flow, Large Elliptic Flow? +/- 90deg v2 < 0 mid-rapidity R OUT/IN = N(90 0 ) + N(270 0 ) N(0 0 ) + N(180 0 ) = 1- 2 V 2 1 + 2 V 2 V 2 = -0.2 → R OUT/IN = 2 ( two times more particles emitted out-of-plane than in the plane ) SIS RHIC

8. R. Lacey, SUNY Stony Brook 8 Where to stop or If Elliptic Flow is very large To balance the minimum a v 4 > (10 v 2 -1)/34 is required v 4 > 4.4% if v 2 =25% STAR, J. Phys. G34 (2007) V 4 ~V 2 2 [ V n ~V 2 n/2 ]

9. R. Lacey, SUNY Stony Brook 9 Excitation function of elliptic flow – Do we understand it ? RHIC SPS SIS GANIL/MSU AGS

10. R. Lacey, SUNY Stony Brook 10 At E/A < 100 MeV: attractive nuclear mean field potential : rotating system of projectile and target b – impact parameter Low energy heavy-ion collisions: E/A=25 MeV

11. R. Lacey, SUNY Stony Brook 11 Excitation function of elliptic flow – 0.4-10 GeV(SIS/AGS) energies SPS SIS AGS Passage time: 2R/(β cm γ cm ) Expansion time: R/c s c s =c√dp/dε - speed of sound ( time for the development of expansion perpendicular to the reaction plane) Delicate balance between: 1) Ability of pressure developed early in the reaction zone to affect a rapid transverse expansion of nuclear matter 2) Passage time for removal of the shadowing of participant hadrons by projectile and target spectators

12. R. Lacey, SUNY Stony Brook 12 If the passage time is long compared to the expansion time (spectator blocking) → squeeze-out x y Azimuthal anisotropy in momentum space (elliptic flow) pxpx pypy  dN/d  -  /2 0  /2

13. R. Lacey, SUNY Stony Brook 13 In-plane elliptic flow (due to pressure gradient) at high beam energies. x y Azimuthal anisotropy in momentum space (elliptic flow) pxpx pypy  dN/d  -  /2 0  /2

14. R. Lacey, SUNY Stony Brook 14 Interplay of passage/expansion times Passage time: 2R/(β cm γ cm ) Expansion time: R/c s c s =c√dp/dε - speed of sound

15. R. Lacey, SUNY Stony Brook 15 Squeeze-out Mechanism Particle emitted in the center-of-mass of the system and moving in a transverse direction with velocity v T will be shadowed by spectators during the passage time: t pass = 2R/(β cm γ cm ) simple geometry estimate → v T t pass /2 > R-b/2 or v T > (1-b/2R) (β cm γ cm ) V2 will increase with v T and impact parameter b (KAOS – Z. Phys. A355 (1996); (E895) - PRL 83 (1999) 1295 Squeeze-out contribution reflects the ratio : c s /(β cm γ cm ) c s =c√dp/dε - speed of sound

16. R. Lacey, SUNY Stony Brook 16 Elliptic Flow@ SIS/AGS Low Energy: Squeeze-out High Energy In-plane

17. R. Lacey, SUNY Stony Brook 17 elliptic flow P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 Determination of the Equation of State of dense matter from collective flow of particles dN/d  1 + 2v 1  cos  + 2v 2 cos2 

18. R. Lacey, SUNY Stony Brook 18 Prologue: Prologue: Constraints for the Hadronic EOS Soft and hard EOS Good Constraints for the EOS achieved Danielewicz, Lacey, Lynch

19. R. Lacey, SUNY Stony Brook 19 Elliptic flow at RHIC b – impact parameter “spectators” Longitudinal and transverse expansion => no influence of spectator matter at midrapidity Passage time: ~ 0.15 fm/c

20. R. Lacey, SUNY Stony Brook 20 ε drives pressure gradients which result in flow. time to thermalize the system (  0 ~ 0.2 - 1 fm/c)  Bjorken  ~ 5 - 15 GeV/fm 3 Thermalization eccentricity PRL87, 052301 (2001) Significant Energy Density is produced in Au+Au collisions at RHIC Substantial elliptic flow signals should be present for a variety of particle species ! Phase Transition:

21. R. Lacey, SUNY Stony Brook 21 Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? Fine Structure of Elliptic Flow at RHIC

22. R. Lacey, SUNY Stony Brook 22 Mass ordering of v2 and ideal fluid hydrodynamics Flavor dependence of v2(pT) enters mainly through mass of the particles → in hydro all particles flow with a common velocity !!! v2 results are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosity  Large cross sections Large cross sections  strong couplings PHENIX : PRL 91, 182301 (2003) STAR : PRC 72, 014904 (2005) p T <1.8 GeV (~ 99% of all particles)

23. R. Lacey, SUNY Stony Brook 23 Elliptic Flow: ultra-cold Fermi-Gas Li-atoms released from an optical (laser) trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions Interaction strength among the atoms can be tuned with an exteranl magnetic field (Feshbach res)  Elliptic flow is a general feature of strongly interacting systems?

24. R. Lacey, SUNY Stony Brook 24 Hadron Gas ? HSD Calculation pT>2 GeV/c Hydrodynamic STAR PHOBOS Hydrodynamic STAR PHOBOS RQMD Hadronic transport models (e.g. RQMD, HSD,...) with hadron formation times ~1 fm/c, fail to describe data. Clearly the system is not a hadron gas.

25. R. Lacey, SUNY Stony Brook 25 Elliptic flow at SPS and ideal hydrodynamics CERES Different picture than at RHIC!?

26. R. Lacey, SUNY Stony Brook 26 Intermediate p T range : Meson vs Baryon Intermediate p T : (2< p T <5 GeV/c): elliptic flow v2(p T ): saturates and tends to depends on the particle species-type ( meson vs baryon) Suppression pattern (R CP or R AA ) is different – meson/baryon effect p/π ratio – more (anti-)protons than pions at intermediate p T ( 2-5 GeV)

27. R. Lacey, SUNY Stony Brook 27 Scaling breaks  Elliptic flow scales with KE T up to KE T ~1 GeV  Indicates hydrodynamic behavior?  Possible hint of quark degrees of freedom become more apparent at higher KE T Baryons scale together Mesons scale together = m T – m Transverse kinetic energy scaling ( WHY ? ) P P PHENIX: Phys. Rev. Lett. 98, 162301 (2007)Phys. Rev. Lett. 98, 162301 (2007)

28. R. Lacey, SUNY Stony Brook 28 v 2 /n q vs KE T /n q scaling works for the full measured range with deviation less than 10% from the universal scaling curve! KE T + Quark number Scaling PHENIX: Phys. Rev. Lett. 98, 162301 (2007)Phys. Rev. Lett. 98, 162301 (2007)

29. R. Lacey, SUNY Stony Brook 29 KE T + Number of constituent Quarks (NCQ) scaling  Scaling seems to hold well for different centralities up to 60% centrality Centrality dependence

30. R. Lacey, SUNY Stony Brook 30 KE T /n scaling and beam energy dependence Au+Au (62.4-200 GeV) STAR Collaboration: Phys. Rev. C 75(2007) 054906

31. R. Lacey, SUNY Stony Brook 31 KE T /n scaling and system size (AuAu/CuCu) KE T /n scaling observed across different colliding systems

32. R. Lacey, SUNY Stony Brook 32 v 4 Scaling The similar scaling for v 4 is found recently at PHENIX. Compatible with partonic flow picture.

33. R. Lacey, SUNY Stony Brook 33 KE T /n Scaling tests at SPS V 2 vs KE T /n scaling breaks at SPS? – the statistical errors are too large : one need to measure v 2 of φ meson at SPS C. Blume (NA49) QM2006 talk

34. R. Lacey, SUNY Stony Brook 34 Elliptic flow of φ meson and partonic collectivity at RHIC.  φ meson has a very small σ for interactions with non-strange particles  φ meson has a relatively long lifetime (~41 fm/c) -> decays outside the fireball  Previous measurements (STAR) have ruled out the K+K- coalescence as φ meson production mechanism -> information should not be changed by hadronic phase  φ is a meson but as heavy as baryons (p, Λ ) :  m(φ)~1.019 GeV/c2 ; (m(p)~0.938 GeV/c2: m(Λ)~1.116 GeV/c2) -> very important test for v2 at intermediate pt ( mass or meson/baryon effect?)

35. R. Lacey, SUNY Stony Brook 35 v2 of φ meson and partonic collectivity at RHIC v 2 vs KE T – is a good way to see if v 2 for the φ follows that for mesons or baryons v 2 /n vs KE T /n scaling clearly works for φ mesons as well nucl-ex/0703024

36. R. Lacey, SUNY Stony Brook 36 Elliptic flow of multistrange hadrons ( φ, Ξ and  ) with their large masses and small hadronic  behave like other particles → consistent with the creation of elliptic flow at partonic level before hadron formation Multi-strange baryon elliptic flow at RHIC (STAR)

37. R. Lacey, SUNY Stony Brook 37 Elliptic flow of D meson All non-photonic electron v2 (pT < 2.0 GeV/c) were assumed to come from D decay D-> e, Pt spectrum constrained by the data Different assumptions for the shape of D meson v2(pt): pion,kaon and proton v2(pt) shapes Measurements and simulations: Shingo Sakai (PHENIX) (See J. Phys G 32, S 551 and his SQM06,HQ06, QM06 talks for details ) Measurements of elliptic flow of non-photonic electrons (PHENIX) Simulations for D meson v2(pt):

38. R. Lacey, SUNY Stony Brook 38 Elliptic flow of D meson: Scaling test The D meson not only flows, it scales over the measured range Heavy-quark relaxation time τR>> τL : τR ~ (Mhq /T)τL ~8 τL for Mhq ~1.4 GeV and T=165 MeV

39. R. Lacey, SUNY Stony Brook 39 Elliptic Flow at RHIC energies For a broad range of reaction centralities (impact parameters) elliptic flow at RHIC energies (62.4-200 GeV) depends only (?) on transverse kinetic energy of the particle KE T and number of valence quarks n q ?

40. R. Lacey, SUNY Stony Brook 40 KE T /n Scaling tests for Ideal Hydro Why Ideal hydro works so bad after close look? - In ideal hydro ( η = 0 !!! )

41. R. Lacey, SUNY Stony Brook 41 protonpion From PHENIX White Paper Nucl. Phys. A757 (2005) 184 Elliptic flow at RHIC and ideal fluid hydrodynamics For p T <1.5 GeV/c V 2 (p T ) and p T spectra of identified hadrons are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosity  Large cross sections Large cross sections  strong couplings Rapid Thermalization ?

42. R. Lacey, SUNY Stony Brook 42 T. Hirano: Highlights from a QGP Hydro + Hadronic Cascade Model hadronic -“ late viscosity” b=7.2fm 0-50% Adapted from S.J.Sanders (BRAHMS) @ QM2006 AuAu200 Hadronic dissipative effects on elliptic flow and spectra

43. R. Lacey, SUNY Stony Brook 43 What is the lowest viscosity at RHIC? Shear viscosity ( η ) – how strongly particles interact and move collectively in a body system. In general, strongly interacting systems have smaller (η) than weakly interacting. But, (η/s) has a lower bound: in standard kinetic theory η=(n λ)/3, where n - proper density, - average total momentum, λ – momentum degradation transport mean free path. The uncertainty principle implies : λ>1/, for relativistic system, the entropy density (s~4n) and (η/s) > 1/12 (η/s) > 1/12 [from “Dissipative Phenomena in Quark-Gluon Plasmas “ P. Danielewicz, M. Gyulassy Phys.Rev. D31, 53,1985. ]Phys.Rev. D31, 53,1985. KSS bound (η/s) > 1/4π

44. R. Lacey, SUNY Stony Brook 44 Constraining  /s with PHENIX data for R AA & v 2 of non-photonic electrons Rapp and van Hees Phys.Rev.C71:034907,2005 Phys.Rev.C71:034907,2005 –Simultaneously describe PHENIX R AA (E) and v 2 (e) with diffusion coefficient in range D HQ (2  T) ~4-6 Moore and Teaney Phys.Rev.C71:064904,2005 Phys.Rev.C71:064904,2005 –Find D HQ /(  /(  +p)) ~ 6 for N f =3 Combining –Recall  +p = T s at  B =0 –This then gives  /s ~(1.5-2)/4  –That is, within factor of 2-3 of conjectured lower bound Phys. Rev. Lett. 98, 172301 (2007)

45. R. Lacey, SUNY Stony Brook 45 Estimation of  /s from RHIC data Damping (flow, fluctuations, heavy quark motion) ~  /s –FLOW:Has the QCD Critical Point Been Signaled by Observations at RHIC?, R. Lacey et al., Phys.Rev.Lett.98:092301,2007 (nucl-ex/0609025)nucl-ex/0609025 –The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553)arXiv:0704.3553 –FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061)nucl-th/0606061 –DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √s NN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)nucl-ex/0611018

46. R. Lacey, SUNY Stony Brook 46 Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007Phys. Rev. Lett. 99:172301, 2007 Calculation: 2 nd order causal viscous hydro: (Glauber IC’s

47. R. Lacey, SUNY Stony Brook 47 T. Hirano: Hydro + Cascade QGP viscosity or hadronic viscosity – both ?

48. R. Lacey, SUNY Stony Brook 48 Small deviations from scaling will yield insights on novel hadronization process. Key Future Test Detector Upgrades + RHIC I AuAu 2 nb -1  baryon (sss) is a stringent test due to the large mass and OZI suppressed hadronic interactions. Example: STAR Time of Flight + DAQ1000

49. R. Lacey, SUNY Stony Brook 49 Viscosity-to-entropy ratio minimum bias Au+Au, √s=200 GeV Lower bound of η/s=1/4 π in the strong coupling limit (P.Kovtun et al. PRL 94 (2005) 111601) L.P.Csernai et al. PRL 97 (2006) 152303; R.Lacey at al. PRL 98 (2007) 092301 η/s for several substances Strong indication for a minimum in the vicinity of T c Partonic fluid Hydrodynamic scaling

50. R. Lacey, SUNY Stony Brook 50 Eccentricity Calculation V 2,M (KE T )= Coalescence/recombination and KE T J.Jia and C. Zhang, Phys. Rev. C 75 (2007) 031901(R) If one modify the momentum conservation relation into kinetic energy conservation relation in the coalescence formula – one will get : 2v 2,q 1+2v 2 2,q KE T /2 ≈ 2 v 2,q ( KE T /2 ) V 2,B (K T )= 3v 2,q +3v 3 2,q 1+6v 2 2,q KE T /3 ≈ 3 v 2,q (KE T /3) mesons baryons Problem with conventional quark coalescence models is energy violation ( 2→ 1, 3→ 1 channels ). What to do with it?

51. R. Lacey, SUNY Stony Brook 51 Quark Coalescence based on a Transport Equation  Resonance formation in quark-(anti)quark scattering as the dominant channel for meson production at RHIC – Energy ( 4-momentum ) conservation satisfied via a finite Γ.  Is it a way to solve the problem? L. Ravagli and R. Rapp: http://arxiv.org/abs/0705.0021

52. R. Lacey, SUNY Stony Brook 52 Constituent Quark Number Scaling (QNS) of v 2 Simple models of hadronization by coalescence/recombination of constituent quarks, which only considers the momentum distribution of quarks and allows quarks with the same p T to coalesce into hadrons → relate quark and hadron v 2 : v 2 p = v 2 h (p T /n)/n, n is the number of quarks in the hadron Models imply  v 2 is developed before hadrons form ( at partonic level ) Coalescence/recombination of constituent quarks can explain both meson/baryon nature of suppression factors and v 2 at intermediate p t Greco, Ko, Levai; Muller, Nonaka, Bass;Hwa,Yang; Molnar, Voloshin

53. R. Lacey, SUNY Stony Brook 53 v 2 (p T /n)/n QNS scaling: close look With higher statistics v 2 measurements, fine structure in QNS is observed: p T >2GeV/c: QNS scaling only works at 20% level p T <2GeV/c: QNS scaling breakes badly with systematic dependence on the hadron mass: it undershoots the v2 values of light mesons and overshoots the v2 values of heavy baryons Imperfections of coalescence/recombination approach? Wrong scaling variable? Can one get a unified description of hadron production and elliptic flow at low and intermediate p T ?

54. R. Lacey, SUNY Stony Brook 54 The idea to use collective flow to Probe the properties of nuclear matter is long-standing W. Scheid, H. Muller, and W. Greiner, PRL 32, 741 (1974) H. Stöcker, J.A. Maruhn, and W. Greiner, PRL 44, 725 (1980) Ne M.I. Sobel, P.J. Siemens, J.P. Bondorf, an H.A. Bethe, Nucl. Phys. A251, 502 (1975) G.F. Chapline, M.H. Johnson, E. Teller, and M.S. Weiss, PRD 8, 4302 (1973) E. Glass Gold et al. Annals of Physics 6, 1 (1959) U

55. R. Lacey, SUNY Stony Brook 55 Summary Universal scaling of the flow of both mesons and baryons (over a broad transverse kinetic energy range) via quark number scaling observed. Development of elliptic flow in the pre-hadronization phase demonstrated Outlook: mechanism of hadronisation at RHIC, what is the range of (η/s) at RHIC?

56. R. Lacey, SUNY Stony Brook 56 Jet Quenching at RHIC Strong quenching of jets, observed in central Au+Au collisions → Evidence of the extreme energy loss of partons traversing matter containing a large density of color charges

57. R. Lacey, SUNY Stony Brook 57 Elliptic flow at RHIC The probe for early time –The dense nuclear overlap is ellipsoid at the beginning of heavy ion collisions –Pressure gradient is largest in the shortest direction of the ellipsoid –The initial spatial anisotropy evolves (via interactions and density gradients )  Momentum-space anisotropy –Signal is self-quenching with time Reaction plane X Z Y PxPx PyPy PzPz