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PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies

PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies. Arkadij Taranenko. Nuclear Chemistry Group SUNY Stony Brook, USA. for the PHENIX Collaboration. Winter Workshop on Nuclear Dynamics Big Sky , MT February 12-17,2007. Why Elliptic Flow ?. Z.

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PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies

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  1. PHENIX Studies of the Scaling Properties of Elliptic Flow at RHIC energies Arkadij Taranenko Nuclear Chemistry Group SUNY Stony Brook, USA for the PHENIX Collaboration Winter Workshop on Nuclear Dynamics Big Sky , MT February 12-17,2007

  2. Why Elliptic Flow ? 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

  3. Resent PHENIX Elliptic Flow Data Detailed differential measurements now available for π, K, p, φ, d, D

  4. RHIC Elliptic Flow Data Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization?

  5. Elliptic flow at RHIC and perfect fluid hydrodynamics The v2 measurements at RHIC are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small ratio of shear viscosity to entropy density η/s ). Looking for scaling properties of elliptic flow in the data – compatible with this picture

  6. Elliptic flow: eccentricity scaling PHENIX article submitted to PRL: nucl-ex/0608033 • Ideal hydro is a scale invariant: v2(pt,b,A)/v2(b,A)~v2(pt) • v2(b,A)/ε(b,A)~const • “Integrated v2 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)

  7. Estimation of the speed of sound See nucl-ex/0604011 for details Eccentricity scaled v2 has a relatively strong dependence on sound speed v2/ε for <pT> ~ 0.45 GeV/c <cs > ~ 0.35 ±0.05 (<cs2 >~ 0.12), soft EOS Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54,2005 <cs > - average value over the time period ~R/cs (the time over the flow develops )

  8. ( WHY ? ) P Transverse kinetic energy scaling Scaling breaks = mT – m Baryons scale together Mesons scale together PHENIX preliminary PHENIX article submitted to PRL: nucl-ex/0608033 • 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

  9. Quark number Scaling PHENIX article submitted to PRL: nucl-ex/0608033 • Apparent Quark number scaling • Hadron mass scaling at low KET (KET < 1 GeV) is preserved. Consistent with quark degrees of freedom in the initial flowing matter

  10. NCQ (pT/n) scaling compared to KET /n NCQ- Scaling PHENIX Preliminary • KET/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

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

  12. KET/n scaling and system size (AuAu/CuCu)

  13. Universal Scaling of Elliptic Flow at RHIC At midrapidity v2 (pt,M,b,A)/n~ F(KET/n)*ε(b,A)? ε(b,A) – integral elliptic flow of charged hadrons KET - transverse kinetic energy n – number of quarks

  14. 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?)

  15. v2 of φ meson and partonic collectivity at RHIC 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

  16. Multi-strange baryon elliptic flow at RHIC (STAR) From M. Oldenburg SQM2006 talk (STAR) J. Phys G 32, S563 (2006) Scaling test 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

  17. Elliptic flow of D meson Robust measurements of elliptic flow of non-photonic electrons (PHENIX) Measurements and simulations: Shingo Sakai (PHENIX) (See J. Phys G 32, S 551 and his SQM06,HQ06, QM06 talks for details ) Simulations for D meson v2(pt): • 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

  18. Elliptic flow of D meson: Scaling test The D meson not only flows, it scales over the measured range

  19. Shear viscosity to entropy density ratio estimate From R. A. Lacey et al. accepted by PRL (nucl-ex/0609025 ) (η/s) ~ (1.1-2.5)/4π

  20. Constraining h/s with PHENIX datafor RAA & v2 of non-photonic electrons PHENIX article submitted to PRL nucl-ex/0611018 • Rapp and van Hees Phys.Rev.C71:034907,2005 • Simultaneously describe PHENIX RAA(E) and v2(e) with diffusion coefficient in range DHQ (2pT) ~4-6 • Moore and Teaney Phys.Rev.C71:064904,2005 • Find DHQ/(h/(e+p)) ~ 6 for Nf=3 • Combining • Recall e+p = T s at mB=0 • This then gives h/s ~(1.5-3)/4p • That is, within factor of 2-3 of conjectured lower bound

  21. Transport Coefficients estimate R. Lacey (nuc-ex/0610029) Moore and Teaney Phys.Rev.C71:064904,2005 D-meson essentially thermal ?

  22. Shear viscosity to entropy density estimates from RHIC data (η/s) ~ (1.1-2.5)/4π R. Lacey et. al., nucl-ex/0609025 (accepted by PRL) “Has the QCD Critical Point been Signaled by Observations at RHIC?”. (η/s) ~ (1.5-3.0)/4π A. Adare et. al., (PHENIX), nucl-ex/0609025 (submitted to PRL) “Energy Loss and Flow of Heavy Quarks in Au+Au collisions at 200 GeV (η/s) ~ (1.0-3.8)/4π S Gavin and M. Abdel-Aziz , Phys. Rev. Lett 97, 162302 (2006) “Measuring Shear Viscosity using transverse momentum correlations”.

  23. 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 • Scaling of D meson v2 compatible with full thermalization of the charm quark observed. • Scaled flow values allow constraints for several transport coefficients. • Outlook:we need to find the range where scaling holds and where it breakes. • .

  24. Elliptic Flow at SPS (Pb+Pb at 158 GeV, NA49) v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 V2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003) C. Blume (NA49) QM2006 talk The statistical errors are too large to make any statement about the scaling of elliptic flow at SPS energies

  25. Comparison with models; RAA & v2for non-photonic electrons (PHENIX) • Two models describes strong suppression and large v2 • Rapp and Van Hees • Elastic scattering -> small heavy quark relaxation time τ • DHQ × 2πT ~ 4 - 6 • Moore and Teaney • DHQ × 2πT = 3~12 • These calculations suggest that small τ and/or DHQare required to reproduce the data. Nucl-ex/0611018

  26. Constraining h/s with PHENIX data • Rapp and van Hees Phys.Rev.C71:034907,2005 • Simultaneously describe PHENIX RAA(E) and v2(e) with diffusion coefficient in range DHQ (2pT) ~4-6 • Moore and Teaney Phys.Rev.C71:064904,2005 • Find DHQ/(h/(e+p)) ~ 6 for Nf=3 • Calculate perturbatively, argue result also plausible non-perturbatively • Combining • Recall e+p = T s at mB=0 • This then gives h/s ~(1.5-3)/4p • That is, within factor of 2 of conjectured bound

  27. Eccentricity Calculation Participant Eccentricity Statistical errors only Au+Au 200 GeV Cu+Cu 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV PHOBOS CollaborationPRL: nucl-ex/0610037 PHOBOS CollaborationPRL: nucl-ex/0610037

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