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Elliptic Flow measurements at RHIC

Elliptic Flow measurements at RHIC. Arkadij Taranenko. Nuclear Chemistry Group SUNY Stony Brook, USA. Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008. Phase diagram (QCD) and RHIC.

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Elliptic Flow measurements at RHIC

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  1. Elliptic Flow measurements at RHIC Arkadij Taranenko Nuclear Chemistry Group SUNY Stony Brook, USA Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008

  2. Phase diagram (QCD) and RHIC How one can probe this new state of matter (QGP)?

  3. One want to see a probe (phenomena) which is • Exist only in Heavy-Ion Collisions (HIC) • Provides reliable estimates of pressure & pressure gradients • Can address questions related to thermalization • Gives insides on the transverse dynamics of the medium • Provides access to the properties of the medium – EOS, viscosity , etc • Well calibrated : measured at Ganil (MSU), SIS, AGS, SPS energies Elliptic Flow in Heavy-Ion Collisions

  4. Elliptic Flow measurements from RHIC to SIS Arkadij Taranenko Nuclear Chemistry Group SUNY Stony Brook, USA Helmholtz International Summer School: “Dense Matter In Heavy Ion Collisions and Astrophysics” Dubna , Russia, July 14-26, 2008

  5. φ=Φ-ΨR y ψR x v2 < 0 mid-rapidity +/- 90deg “Squeeze-Out” - First Elliptic flow signal in HIC Diogene, M. Demoulins et al., Phys. Lett. B241, 476 (1990) Plastic Ball, H.H. Gutbrod et al., Phys. Lett. B216, 267 (1989) Reaction plane Reaction Plane

  6. φ=Φ-ΨR y ψR x v1 < 0 v2 < 0 mid-rapidity Fourier decomposition of single particle (semi) inclusive spectra: +/- 90deg +/- 180deg Directed flow Elliptic flow KAOS Cheuk-Yin WONG , Physics Letters, 88B, p 39 (1979) Sergei Voloshin, Y. Zhang, Z. Phys. C70,(1996), 665

  7. v2 < 0 mid-rapidity +/- 90deg Small Elliptic flow, Large Elliptic Flow? SIS V2= -0.2 → ROUT/IN = 2 ( two times more particles emitted out-of-plane than in the plane ) 1- 2 V2 N(900) + N(2700) ROUT/IN= = N(00) + N(1800) 1 + 2 V2 RHIC

  8. Where to stop or If Elliptic Flow is very large To balance the minimum a v4 > (10v2-1)/34 is required v4 > 4.4% if v2=25% STAR, J. Phys. G34 (2007) V4~V22 [ Vn~V2n/2 ]

  9. Excitation function of elliptic flow – Do we understand it ? RHIC GANIL/MSU SPS AGS SIS

  10. b – impact parameter At E/A < 100 MeV: attractive nuclear mean field potential : rotating system of projectile and target Low energy heavy-ion collisions: E/A=25 MeV

  11. Excitation function of elliptic flow – 0.4-10 GeV(SIS/AGS) energies Passage time: 2R/(βcmγcm) Expansion time:R/cs cs=c√dp/dε - speed of sound ( time for the development of expansion perpendicular to the reaction plane) AGS SPS SIS Delicate balance between: 1) Ability of pressure developed early in the reaction zone to affect a rapid transverse expansion of nuclear matter 2) Passage time for removal of the shadowingof participant hadrons by projectile and target spectators

  12. py px dN/d y  -/2 0 /2 x If the passage time is long compared to the expansion time (spectator blocking) → squeeze-out Azimuthal anisotropy in momentum space (elliptic flow)

  13. py px dN/d y  -/2 0 /2 x In-plane elliptic flow (due to pressure gradient) at high beam energies. Azimuthal anisotropy in momentum space (elliptic flow)

  14. Interplay of passage/expansion times Passage time: 2R/(βcmγcm) Expansion time:R/cs cs=c√dp/dε - speed of sound

  15. (KAOS – Z. Phys. A355(1996); (E895) - PRL 83(1999) 1295 Squeeze-out Mechanism Particle emitted in the center-of-mass of the system and moving in a transverse direction with velocity vT will be shadowed by spectators during the passage time: tpass=2R/(βcmγcm)simple geometry estimate→vTtpass/2 > R-b/2or vT > (1-b/2R) (βcmγcm) V2 will increase with vT and impact parameter b Squeeze-out contribution reflects the ratio : cs/(βcm γcm) cs=c√dp/dε - speed of sound

  16. Elliptic Flow@ SIS/AGS Low Energy: Squeeze-out High Energy In-plane

  17. Determination of the Equation of State of dense matter from collective flow of particles P. Danielewicz, R. Lacey, W.G. Lynch, Science 298 (2002) 1592 elliptic flow dN/dF  (1 + 2v1cosF + 2v2 cos2F)

  18. Danielewicz, Lacey, Lynch Good Constraints for the EOS achieved Soft and hard EOS Prologue: Constraints for the Hadronic EOS

  19. “spectators” b – impact parameter “spectators” Elliptic flow at RHIC Longitudinal and transverse expansion => no influence of spectator matter at midrapidity Passage time: ~ 0.15 fm/c

  20. Phase Transition: Significant Energy Density is produced in Au+Au collisions at RHIC Thermalization PRL87, 052301 (2001) eccentricity time to thermalize the system (t0 ~ 0.2 - 1 fm/c) eBjorken~ 5 - 15 GeV/fm3 ε drives pressure gradients which result in flow. Substantial elliptic flow signals should be present for a variety of particle species !

  21. 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?

  22. Mass ordering of v2 and ideal fluid hydrodynamics PHENIX : PRL 91, 182301 (2003) STAR : PRC 72, 014904 (2005) pT<1.8 GeV (~ 99% of all particles) Flavor dependence of v2(pT) enters mainly through mass of the particles → in hydro all particles flow with a common velocity !!! v2 results are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosityLarge cross sections Large cross sections strong couplings

  23. Elliptic Flow: ultra-cold Fermi-Gas • Li-atoms released from an optical (laser) trap exhibit elliptic flow analogous to what is observed in ultra-relativistic heavy-ion collisions • Interaction strength among the atoms can be tuned with an exteranl magnetic field (Feshbach res) • Elliptic flow is a general feature of strongly interacting systems?

  24. Hadronic transport models (e.g. RQMD, HSD, ...) with hadron formation times ~1 fm/c, fail to describe data. Hydrodynamic STAR PHOBOS HSD Calculation pT>2 GeV/c RQMD Hadron Gas ? Clearly the system is not a hadron gas.

  25. Elliptic flow at SPS and ideal hydrodynamics CERES Different picture than at RHIC!?

  26. Intermediate pT range : Meson vs Baryon • Intermediate pT : (2< pT<5 GeV/c): • elliptic flow v2(pT): saturates and tends to depends on the particle species-type ( meson vs baryon) • Suppression pattern (RCP orRAA) is different – meson/baryon effect • p/π ratio – more (anti-)protons than • pions at intermediate pT ( 2-5 GeV)

  27. ( WHY ? ) P Transverse kinetic energy scaling Scaling breaks = mT – m Baryons scale together Mesons scale together PHENIX: Phys. Rev. Lett. 98, 162301 (2007) • Elliptic flow scales with KET up to KET ~1 GeV • Indicates hydrodynamic behavior? • Possible hint of quark degrees of freedom become more apparent at higher KET

  28. KET + Quark number Scaling PHENIX: Phys. Rev. Lett. 98, 162301 (2007) v2 /nq vs KET/nq scaling works for the full measured range with deviation less than 10% from the universal scaling curve!

  29. KET + Number of constituent Quarks (NCQ) scaling Centrality dependence • Scaling seems to hold well for different centralities up to 60% centrality

  30. KET/n scaling and beam energy dependence Au+Au (62.4-200 GeV) STAR Collaboration: Phys. Rev. C 75(2007) 054906

  31. KET/n scaling and system size (AuAu/CuCu) KET/n scaling observed across different colliding systems

  32. v4 Scaling • The similar scaling for v4 is found recently at PHENIX. • Compatible with partonic flow picture.

  33. KET/n Scaling tests at SPS C. Blume (NA49) QM2006 talk V2 vs KET/n scaling breaks at SPS? – the statistical errors are too large : one need to measure v2 of φ meson at SPS

  34. 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 (STAR) 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?)

  35. v2 of φ meson and partonic collectivity at RHIC nucl-ex/0703024 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

  36. Multi-strange baryon elliptic flow at RHIC (STAR) 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 at partonic level before hadron formation

  37. Elliptic flow of D meson 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

  38. Elliptic flow of D meson: Scaling test Heavy-quark relaxation time τR>> τL : τR ~ (Mhq /T)τL ~8 τL for Mhq ~1.4 GeV and T=165 MeV The D meson not only flows, it scales over the measured range

  39. Elliptic Flow at RHIC energies For a broad range of reaction centralities (impact parameters) elliptic flow at RHIC energies (62.4-200 GeV) depends only (?) on transverse kinetic energy of the particle KET and number of valence quarks nq ?

  40. KET/n Scaling tests for Ideal Hydro Why Ideal hydro works so bad after close look? - In ideal hydro ( η = 0 !!! )

  41. proton pion Elliptic flow at RHIC and ideal fluid hydrodynamics From PHENIX White Paper Nucl. Phys. A757 (2005) 184 Rapid Thermalization ? For pT <1.5 GeV/c V2(pT) and pT spectra of identified hadrons are in a good agreement with the predictions of ideal relativistic hydrodynamics ( rapid thermalization t< 1fm/c and an extremely small η/s ) → small viscosityLarge cross sections Large cross sections strong couplings

  42. T. Hirano: Highlights from a QGP Hydro + Hadronic Cascade Model Hadronic dissipative effects on elliptic flow and spectra AuAu200 Adapted from S.J.Sanders (BRAHMS) @ QM2006 b=7.2fm 0-50% hadronic -“ late viscosity”

  43. What is the lowest viscosity at RHIC? Shear viscosity (η) – how strongly particles interact and move collectively in a body system. In general, strongly interacting systems have smaller (η) than weakly interacting. But, (η/s) has a lower bound: in standard kinetic theory η=(n<p>λ)/3 , where n - proper density , <p>- average total momentum, λ – momentum degradation transport mean free path. The uncertainty principle implies : λ>1/<p> , for relativistic system, the entropy density (s~4n) and (η/s) > 1/12 (η/s) > 1/12 [from “Dissipative Phenomena in Quark-Gluon Plasmas “ P. Danielewicz, M. Gyulassy Phys.Rev. D31, 53,1985.] KSS bound (η/s) > 1/4π

  44. Constraining h/s with PHENIX datafor RAA & v2 of non-photonic electrons Phys. Rev. Lett. 98, 172301 (2007) • 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 ~(1.5-2)/4p • That is, within factor of 2-3 of conjectured lower bound

  45. Estimation of h/s from RHIC data • Damping (flow, fluctuations, heavy quark motion) ~ h/s • FLOW:Has the QCD Critical Point Been Signaled by Observations at RHIC?,R. Lacey et al., Phys.Rev.Lett.98:092301,2007(nucl-ex/0609025) • The Centrality dependence of Elliptic flow, the Hydrodynamic Limit, and the Viscosity of Hot QCD, H.-J. Drescher et al., (arXiv:0704.3553) • FLUCTUATIONS: Measuring Shear Viscosity Using Transverse Momentum Correlations in Relativistic Nuclear Collisions, S. Gavin and M. Abdel-Aziz, Phys.Rev.Lett.97:162302,2006 (nucl-th/0606061) • DRAG, FLOW: Energy Loss and Flow of Heavy Quarks in Au+Au Collisions at √sNN = 200 GeV (PHENIX Collaboration), A. Adare et al., to appear in Phys. Rev. Lett. (nucl-ex/0611018)

  46. Viscosity Information from Relativistic Nuclear Collisions: How Perfect is the Fluid Observed at RHIC?, P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99:172301, 2007 • Calculation:2nd order causal viscous hydro: (Glauber IC’s

  47. T. Hirano: Hydro + Cascade QGP viscosity or hadronic viscosity – both ?

  48. Detector Upgrades + RHIC I AuAu 2 nb-1 Example: STAR Time of Flight + DAQ1000 Key Future Test W baryon (sss) is a stringent test due to the large mass and OZI suppressed hadronic interactions. Small deviations from scaling will yield insights on novel hadronization process.

  49. η/s for several substances Strong indication for a minimum in the vicinity of Tc L.P.Csernai et al. PRL 97 (2006) 152303; R.Lacey at al. PRL 98 (2007) 092301 Viscosity-to-entropy ratio minimum bias Au+Au, √s=200 GeV Hydrodynamic scaling Partonic fluid Lower bound of η/s=1/4π in the strong coupling limit (P.Kovtun et al. PRL 94 (2005) 111601)

  50. Eccentricity Calculation Coalescence/recombination and KET J.Jia and C. Zhang, Phys. Rev. C 75 (2007) 031901(R) If one modify the momentum conservation relation into kinetic energy conservation relation in the coalescence formula – one will get : 2v2,q ≈ 2 v2,q ( KET/2 ) mesons V2,M(KET)= 1+2v22,q KET/2 3v2,q+3v32,q ≈ 3 v2,q(KET/3) baryons V2,B(KT)= 1+6v22,q KET/3 Problem with conventional quark coalescence models is energy violation ( 2→ 1, 3→ 1 channels ). What to do with it?

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