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

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

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

R. Lacey, SUNY Stony Brook 4 Substantial elliptic flow signals are observed for a variety of particle species at RHIC. Indication of rapid thermalization? RHIC Elliptic Flow Data

R. Lacey, SUNY Stony Brook 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

R. Lacey, SUNY Stony Brook 6 Elliptic flow: eccentricity scaling Ideal hydro is a 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) PHENIX article submitted to PRL: nucl-ex/

R. Lacey, SUNY Stony Brook 7 Estimation of the speed of sound ~ 0.35 ± 0.05 ( ~ 0.12), so ft EOS v 2 /ε for ~ 0.45 GeV/c See nucl-ex/ for details Eccentricity scaled v2 has a relatively strong dependence on sound speed Bhalerao, Blaizot, Borghini, Ollitrault : Phys.Lett.B627:49-54, average value over the time period 2R/cs ( the time over the flow develops )

R. Lacey, SUNY Stony Brook 8 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 PHENIX article submitted to PRL: nucl-ex/

R. Lacey, SUNY Stony Brook 9  Apparent Quark number scaling  Hadron mass scaling at low KE T (KE T < 1 GeV) is preserved. Quark number Scaling PHENIX article submitted to PRL: nucl-ex/ Consistent with quark degrees of freedom in the initial flowing matter

R. Lacey, SUNY Stony Brook 10 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

R. Lacey, SUNY Stony Brook 11 KE T /n scaling across collision centralities KE T /n scaling observed across centralities

R. Lacey, SUNY Stony Brook 12 KE T /n scaling and system size (AuAu/CuCu)

R. Lacey, SUNY Stony Brook 13 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

R. Lacey, SUNY Stony Brook 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?)

R. Lacey, SUNY Stony Brook 15 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

R. Lacey, SUNY Stony Brook 16 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) STAR preliminary 200 GeV Au+Au From M. Oldenburg SQM2006 talk (STAR) J. Phys G 32, S563 (2006) Scaling test

R. Lacey, SUNY Stony Brook 17 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 ) Robust measurements of elliptic flow of non-photonic electrons (PHENIX) Simulations for D meson v2(pt):

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

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

R. Lacey, SUNY Stony Brook 20 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 ~(1.5-3)/4  –That is, within factor of 2-3 of conjectured lower bound PHENIX article submitted to PRL nucl-ex/

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

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

R. Lacey, SUNY Stony Brook 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 v 2 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. –.

R. Lacey, SUNY Stony Brook 24 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/ C. Blume (NA49) QM2006 talk

R. Lacey, SUNY Stony Brook 25 Comparison with models; R AA & v 2 for non-photonic electrons (PHENIX) Two models describes strong suppression and large v 2 Rapp and Van Hees Elastic scattering -> small heavy quark relaxation time τ D HQ × 2πT ~ Moore and Teaney D HQ × 2πT = 3~12 These calculations suggest that small τ and/or D HQ are required to reproduce the data. Nucl-ex/

R. Lacey, SUNY Stony Brook 26 Constraining  /s with PHENIX data 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 –Calculate perturbatively, argue result also plausible non-perturbatively Combining –Recall  +p = T s at  B =0 –This then gives  /s ~(1.5-3)/4  –That is, within factor of 2 of conjectured bound