Scaling Properties of Elliptic Flow at RHIC energies

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

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 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 Z Reaction plane Y X

hadronic phase and freeze-out QGP and hydrodynamic expansion initial state pre-equilibrium hadronization 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 Time

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

Elliptic Flow at RHIC Z • 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 Y X Pz Py Px

PRL87, 052301 (2001) Extrapolation From ET Distributions peripheral collisions Central collisions time to thermalize the system (t0 ~ 0.2 - 1 fm/c) eBjorken~ 5 - 15 GeV/fm3 ~ 35 – 100 ε0 Phase Transition: Reminder High Energy density matter is created at RHIC! The Energy Density is Well Above the Predicted Value for the Phase Transition /crossover !

Reminder Statistical Model Comparisons of Particle Ratios Hadro-chemistry indicates a single Hadronization Temperature ~ 175 MeV

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

Extrapolation From ET Distributions Large Pressure Gradients v2 Detailed integral and differential Measurements now available for Is Thermalization Rapid ? Self quenching Substantial elliptic flow signals should be present for a variety of particle species !

Fine Structure of Elliptic Flow at RHIC Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? PHENIX : PRL 91, (2003)

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.

Is thermalization achieved ? • Large v2 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: v2 /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

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

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 v2 • “Integrated v2 reflects momentum anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano nucl-th/050604) • Integrated v2 is proportional to the eccentricity STAR

Eccentricity scaling of elliptic flow Data Scaling tests v2 (pt,b)/ε(b)~v2(pt) v2(pt/b)/v2(b)~v2(pt) V2(b)/ε(b)~const

Eccentricity scaling and system size Data Scaling test PHENIX Preliminary PHENIX Preliminary v2 scales with eccentricity and across system size

Sound speed & Eccentricity scaled v2 Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005 Eccentricity scaled v2 has a relatively strong dependence on cs

F. Karsch, hep-lat/0601013 Speed of sound Estimate v2/ε for <pT> ~ 0.45 GeV/c cs ~ 0.35 ±0.05 (cs2 ~ 0.12), soft EOS 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

Beam Energy dependence of elliptic flow (PHENIX) Phys.Rev.Lett.94:232302,2005 • Saturation of the differential elliptic flow is observed at RHIC energies • Compatible with soft EoS

Scaling breaks Baryons scale together Mesons scale together ( WHY ? ) P Transverse kinetic energy scaling PHENIX preliminary • Elliptic flow scales with KET up to KET ~1 GeV • Indicates hydrodynamic behavior • Possible hint of quark degrees of freedom become apparent at higher KET

Quark number Scaling nucl-ex/0604011 PHENIX preliminary • Apparent Quark number scaling • Hadron mass scaling at low KET (KET < 1 GeV) is preserved. Consitent with quark degrees of freedom in the initial flowing matter

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?)

Elliptic flow of resonance particles Before subtraction Signal + Background Background After subtraction 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)

Elliptic Flow of φ meson at RHIC (Scaling tests) v2 vs KET – is a good way to see if v2 for the φ follows that for mesons or baryons v2/n vs KET/n scaling clearly works for φmesons as well

Multi-strange baryon elliptic flow at RHIC Scaling test From M. Oldenburg SQM2006 talk (STAR) STAR preliminary 200 GeV Au+Au Elliptic flow of multistrange hadrons (φ, Ξand  ) with their large masses and small hadronic s behave like other particles → consistentwith the creation of elliptic flow on partonic level before hadron formation

KET/n scaling across collision centralities KET/n scaling observed across centralities

Universal Scaling of Elliptic Flow at RHIC At midrapidity v2 (pt,M,b,A)/n~ F(KET/n)*eccentricity(b,A)?

Shear viscosity to entropy density ratio at RHIC See nucl-ex/0609025, 0608046 for details

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 KET (<=1GeV) and separately at higher KET , showing the relevance of the quark degrees of freedom • Scaling with KET/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

Scaling Properties of Elliptic Flow at RHIC energies