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R. Lacey, SUNY Stony Brook 1 Arkadij Taranenko Quark Matter 2006 November 13-20, Shanghai, China Nuclear Chemistry Group SUNY Stony Brook, USA PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies for the PHENIX Collaboration

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R. Lacey, SUNY Stony Brook 2 Why Elliptic Flow ? 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

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R. Lacey, SUNY Stony Brook 3 PHENIX Elliptic Flow Data Detailed differential measurements now available for π, K, p, φ, d, D

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R. Lacey, SUNY Stony Brook 4 PHENIX Elliptic Flow Data (Posters) Energy and System Size dependence of Elliptic flow at RHIC (AuAu/CuCu at GeV) in the poster of Maya Shimomura : “Measurement of Azimuthal Anisotropy for High Pt charged hadrons at RHIC-PHENIX”. Poster 38, Room 104 Wind Energy Room Differential Elliptic flow measurements at forward rapidities in the poster of I. J. Choi : “Inclusive single muon flow for Au+Au collisions at 200 GeV in the PHENIX experiment at RHIC” Poster 13, Room 104 Wind Energy Room

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R. Lacey, SUNY Stony Brook 5 Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? RHIC Elliptic Flow Data PHENIX : PRL 91, (2003)

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R. Lacey, SUNY Stony Brook 6 Universal Scaling of Elliptic Flow at RHIC ε(b,A) – integral elliptic flow of charged hadrons At midrapidity v 2 (pt,M,b,A)/n~ F(KE T /n)*ε(b,A)? KE T - transverse kinetic energy n – number of quarks

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R. Lacey, SUNY Stony Brook 7 Elliptic flow: eccentricity scaling Ideal hydro is scale invariant: v2(pt,b,A)/v2(b,A)~v2(pt) v2(b,A)/ε(b,A)~const “Integrated v 2 reflects momentum anisotropy of bulk matter and saturates within the first 3-4 fm/c just after collision” (Gyulassy,Hirano Nucl.Phys.A769:71-94,2006) In hydro models integrated v 2 is proportional to the eccentricity Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005

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R. Lacey, SUNY Stony Brook 8 Eccentricity scaling and system size v 2 scales with eccentricity and across system size Scaling test nucl-ex/ k ~ 3.1+/-0.2 obtained from data New PHENIX article on the scaling properties of elliptic flow: nucl-ex/ For Au+Au collisions the eccentricity from Glauber model ε=k v2(centrality)

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R. Lacey, SUNY Stony Brook 9 Sound speed & Eccentricity scaled v 2 Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005 Eccentricity scaled v2 has a relatively strong dependence on sound speed

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R. Lacey, SUNY Stony Brook 10 c s ~ 0.35 ± 0.05 (c s 2 ~ 0.12), so ft EOS F. Karsch, hep-lat/ v 2 /ε for ~ 0.45 GeV/c See nucl-ex/ for details An effective EOS is softer than that for high temperature QGP, but does not reflect a strong first order phase transition, where Cs=0 during an extended hadronization period Sound speed & Eccentricity scaled v2

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R. Lacey, SUNY Stony Brook 11 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 = m T – m Transverse kinetic energy scaling ( WHY ? ) P P New PHENIX article on the scaling properties of elliptic flow: nucl-ex/

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R. Lacey, SUNY Stony Brook 12 Apparent Quark number scaling Hadron mass scaling at low KE T (KE T < 1 GeV) is preserved. Quark number Scaling New PHENIX article on the scaling properties of elliptic flow: nucl-ex/ Consistent with quark degrees of freedom in the initial flowing matter

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R. Lacey, SUNY Stony Brook 13 NCQ (p T /n) scaling compared to KE T /n KE T /n scaling works for the full measured range with deviation less than 10% from the universal scaling curve NCQ- scaling works only at 20% level for pt>2 GeV/c and breakes below with clear systematic dependence on the mass PHENIX Preliminary NCQ- Scaling

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R. Lacey, SUNY Stony Brook 14 KE T /n scaling across collision centralities KE T /n scaling observed across centralities

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R. Lacey, SUNY Stony Brook 15 KE T /n scaling and system size (AuAu/CuCu)

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R. Lacey, SUNY Stony Brook 16 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 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?)

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R. Lacey, SUNY Stony Brook 17 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

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R. Lacey, SUNY Stony Brook 18 Elliptic flow of D meson The D meson not only flows, it scales over the measured range expected D meson v2 from non-photonic electron v2 (pT < 2.0 GeV/c) Simulations: Shingo Sakai (PHENIX) (See SQM2006, HQ2006 Talks and proceedings for details) See Talk of Shingo Sakai (Parallel 2.1, Sat 3:20 pm )

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R. Lacey, SUNY Stony Brook 19 Shear viscosity to entropy density ratio estimate From R. A. Lacey et al. submitted to PRL (nucl-ex/ ) and nucl-ex/ PHENIX estimate of η/s from the comparison of the measured RAA and v2 of non-photonic electrons with models: η/s ~(1.5-3)/4π, see Talk of Shingo Sakai (Parallel 2.1, Sat 3:20 pm ) (η/s) ~ ( )/4π

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R. Lacey, SUNY Stony Brook 20 Elliptic Flow at SPS (Pb+Pb at 158 GeV, NA49) The statistical errors are too large to make any statement about the scaling of elliptic flow at SPS energies V2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/ ) v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/ submitted to PRL

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R. Lacey, SUNY Stony Brook 21 Summary Scaling predictions of perfect fluid hydrodynamics for the elliptic flow coefficient v 2 tested and validated Development of elliptic flow in the pre-hadronization phase demonstrated Scaling of D meson v 2 compatible with full thermalization of the charm quark observed. Universal scaling of the flow of both mesons and baryons (over a broad transverse kinetic energy range) via quark number scaling observed. Scaled flow values allow constraints for several transport coefficients. Outlook: we need to find the range where scaling holds and where it breakes. –. Results compatible with a plasma having essentially perfect liquid-like properties

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R. Lacey, SUNY Stony Brook 22 Backup Slides

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R. Lacey, SUNY Stony Brook 23 Buda-Lund Model nucl-th/ R.Lacey, QM2005 Equivalent to a kinetic energy Non-relativistic expression Looking for scaling properties for v 2 Relativistic effects are important especially for light particles Hence, use relativistic formula Scaling breaks for kaons

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R. Lacey, SUNY Stony Brook 24 3-D Hydro C. Nonaka R. Fries, SQM2006 Quark number and quark mass scaling are not incompatible Mass scaling from hydrodynamics is not perturbed by consituent quark scaling KE T /n scaling and hydrodynamics

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R. Lacey, SUNY Stony Brook 25 Universal Scaling of Elliptic Flow at RHIC!!! See Tamas Csorgo talk on Wednesday ! M.Csanad, T.Csorgo et al nucl-th/ Nucl.Phys.A742:80-94,2004

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R. Lacey, SUNY Stony Brook 26 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

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