1. R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko XVIII Baldin ISHEPP September 25-30, JINR Dubna Nuclear Chemistry Group SUNY Stony Brook, USA Scaling Properties of Elliptic Flow at RHIC energies

2. R. Lacey, SUNY Stony Brook 2 Goal of HIC experiments at RHIC: To create and study Quark-Gluon Plasma (QGP) – a state of deconfined, thermalized quark and gluons over a large volume predicted by QCD at high energy density Reaction plane X Z Y Elliptic flow is a common term for the second harmonic in particle azimuthal distribution relative to the reaction plane, the plane spanned by the beam direction and impact parameter vector

3. R. Lacey, SUNY Stony Brook 3 Outline  Introduction: why elliptic flow measurements are very important for study properties of QGP at RHIC?  Fine structure of elliptic flow for particles produced at midrapidity: v2 = f ( pt, centrality, system, energy..)  Scaling of elliptic flow at RHIC  What can we learn from scaling characteristics of elliptic flow ?  Summary and outlook initial state pre-equilibrium QGP and hydrodynamic expansion hadronization hadronic phase and freeze-out Time

4. R. Lacey, SUNY Stony Brook 4 The transition from in-plane to out-of-plane and back to in-plane emission Is understood The Rich Structure of the Integral Flow Excitation Function Soft and hard EOS Good Constraints for the EOS achieved Danielewicz, Lacey, Lynch

5. R. Lacey, SUNY Stony Brook 5 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

6. R. Lacey, SUNY Stony Brook 6 PRL87, 052301 (2001) Central collisions peripheral collisions time to thermalize the system (  0 ~ 0.2 - 1 fm/c)  Bjorken  ~ 5 - 15 GeV/fm 3 ~ 35 – 100 ε 0 Extrapolation From E T Distributions The Energy Density is Well Above the Predicted Value for the Phase Transition /crossover ! Phase Transition:Reminder High Energy density matter is created at RHIC! Reminder High Energy density matter is created at RHIC!

7. R. Lacey, SUNY Stony Brook 7 Reminder Statistical Model Comparisons of Particle RatiosReminder Statistical Model Comparisons of Particle Ratios Hadro-chemistry indicates a single Hadronization Temperature ~ 175 MeV

8. R. Lacey, SUNY Stony Brook 8 Cu+Cu Preliminary 3-6%, N part = 100 Au+Au 35-40%, N part = 99 dN/d  very similar for Au+Au and Cu+Cu at same Npart Multiplicity distribution follows the independence hypothesis ! Is Thermalization Achieved ? Is Thermalization Achieved ? Au+Au 35-40%,N part = 98 Cu+Cu Preliminary 3-6%, N part = 96 PHOBOS Data Measure property as a function of system size

9. R. Lacey, SUNY Stony Brook 9 Substantial elliptic flow signals should be present for a variety of particle species ! Extrapolation From E T Distributions Is Thermalization Rapid ? Is Thermalization Rapid ? Large Pressure Gradients v 2 Detailed integral and differential Measurements now available for Self quenching

10. R. Lacey, SUNY Stony Brook 10 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 PHENIX : PRL 91, (2003)

11. R. Lacey, SUNY Stony Brook 11 Exploring Scaling properties of Elliptic Flow Scaling properties in science relate macroscopic observables to underlying system properties  In heavy-ion collisions, they can serve to find simple laws relating measured anisotropy to system properties and/or degrees of freedom  Eccentricity scaling and thermalization  Transverse kinetic energy and constituent quark number scaling  What can be learnt from these scaling properties ? If Elliptic flow Is a collective effect we should see its scaling properties in the data.

12. R. Lacey, SUNY Stony Brook 12 Is thermalization achieved ?  Large v 2 indicative of high degree of thermalization of produced matter at RHIC  Are there other observables showing that the matter is thermalized ?  Ideal hydrodynamics is scale invariant. If the matter behaves hydrodynamicaly and is thermalized: v 2 /ε should be independent of centrality and size of colliding systems  Do we observe such independence in the data?  Data for different colliding systems (Au+Au, Cu+Cu) are available to test this

13. R. Lacey, SUNY Stony Brook 13 Eccentricity scaling in Hydro Eccentricity scaling observed in hydrodynamic model over a broad range of centralities R: measure of size of system Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005 This is a clear test that can be applied to data !

14. R. Lacey, SUNY Stony Brook 14 Elliptic flow: eccentricity scaling  Ideal hydro is scale invariant and v2 (b,A)/ε(b,A)~const  For eccentricity scaling test one need Glauber Model calculations or one can also use experimental quantity sensitive to initial eccentricity, like the integrated v 2  “Integrated v 2 reflects momentum anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano nucl- th/050604)  Integrated v 2 is proportional to the eccentricity STAR

15. R. Lacey, SUNY Stony Brook 15 Eccentricity scaling of elliptic flow v2 (pt,b)/ε(b)~v2(pt) v2(pt/b)/v2(b)~v2(pt) V2(b)/ε(b)~const DataScaling tests

16. R. Lacey, SUNY Stony Brook 16 Eccentricity scaling and system size v 2 scales with eccentricity and across system size PHENIX Preliminary Data Scaling test

17. R. Lacey, SUNY Stony Brook 17 Sound speed & Eccentricity scaled v 2 Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005 Eccentricity scaled v 2 has a relatively strong dependence on c s

18. R. Lacey, SUNY Stony Brook 18 Speed of sound Estimate c s ~ 0.35 ± 0.05 (c s 2 ~ 0.12), so ft EOS F. Karsch, hep-lat/0601013 v 2 /ε for ~ 0.45 GeV/c See nucl-ex/0604011 for details The EOS is harder than that for the hadron gas but softer than that for QGP  no strong first order phase transition

19. R. Lacey, SUNY Stony Brook 19 Beam Energy dependence of elliptic flow  Saturation of the differential elliptic flow is observed at RHIC energies  Compatible with soft EoS Phys.Rev.Lett.94:232302,2005 (PHENIX)

20. R. Lacey, SUNY Stony Brook 20 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 apparent at higher KE T Baryons scale together Mesons scale together PHENIX preliminary Transverse kinetic energy scaling ( WHY ? ) P P

21. R. Lacey, SUNY Stony Brook 21  Apparent Quark number scaling  Hadron mass scaling at low KE T (KE T < 1 GeV) is preserved. PHENIX preliminary Quark number Scaling nucl-ex/0604011 Consitent with quark degrees of freedom in the initial flowing matter

22. R. Lacey, SUNY Stony Brook 22 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 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?)

23. R. Lacey, SUNY Stony Brook 23 Signal + Background Background Before subtraction After subtraction Elliptic flow of resonance particles Using the robust method for study the elliptic flow of resonance particle developed by N. Borghini and J.Y. Ollitrault (Phys.Rev.C70:064905,2004) N. BorghiniJ.Y. Ollitrault

24. R. Lacey, SUNY Stony Brook 24 Elliptic Flow of φ meson at RHIC (Scaling tests) 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

25. R. Lacey, SUNY Stony Brook 25 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 on partonic level before hadron formation Multi-strange baryon elliptic flow at RHIC STAR preliminary 200 GeV Au+Au From M. Oldenburg SQM2006 talk (STAR) Scaling test

26. R. Lacey, SUNY Stony Brook 26 KE T /n scaling across collision centralities KE T /n scaling observed across centralities

27. R. Lacey, SUNY Stony Brook 27 Universal Scaling of Elliptic Flow at RHIC At midrapidity v 2 (pt,M,b,A)/n~ F(KE T /n)*eccentricity(b,A)?

28. R. Lacey, SUNY Stony Brook 28 Shear viscosity to entropy density ratio at RHIC See nucl-ex/0609025, 0608046 for details

29. R. Lacey, SUNY Stony Brook 29 Summary  Eccentricity scaling holds over a broad range of centralities and is indicative of thermalization of matter produced at RHIC  Hydrodynamic model comparison leads to an estimate of the speed of sound. Data compatible with soft EOS  Transverse kinetic energy is an appropriate variable to scale elliptic flow; related to pressure gradients  Baryons and mesons scale together at low KE T (<=1GeV) and separately at higher KE T, showing the relevance of the quark degrees of freedom  Scaling with KE T /n leads to the universal scaling of elliptic flow – evidence of partonic origin of elliptic flow at RHIC -> transverse expansion of the matter is generated during the phase in which it contains independent quasi particles with quantum number of quarks