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QM2009 summary: Soft physics: Flow and hydrodynamics

QM2009 summary: Soft physics: Flow and hydrodynamics. A. Marin (GSI). OUTLINE. HBT Flow Hydrodynamics. HBT PUZZLE (S. Pratt). RHIC HBT PUZZLE: flow & spectra OK HBT radii NOT OK ideal hydro (no viscosity) 1st order phase transition  0 =1.0 fm/c. HBT PUZZLE (S. Pratt).

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QM2009 summary: Soft physics: Flow and hydrodynamics

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  1. QM2009 summary: Soft physics: Flow and hydrodynamics A. Marin (GSI)

  2. OUTLINE • HBT • Flow • Hydrodynamics

  3. HBT PUZZLE (S. Pratt) RHIC HBT PUZZLE: flow & spectra OK HBT radii NOT OK ideal hydro (no viscosity) 1st order phase transition 0 =1.0 fm/c

  4. HBT PUZZLE (S. Pratt) S. Pratt, arXiv:0812.4714v1 Solution: Early acceleration (t < 1 fm/c) Shear viscosity EoS (crossover) Initial energy profile Fixing HBT requires increasing explosivity Bulk viscosity decreases radial flow Early flow increases elliptic flow viscosity decreases elliptic flow

  5. Effect of Eccentricity Fluctuationsand Nonflow on Elliptic Flow Methods Jean-Yves Ollitrault, Art Poskanzer, and Sergei Voloshin QM09

  6. Reaction, Participant, and Event Planes momentum space coordinate space participant plane

  7. Methods review of azimuthal anisotropy: arXiv: 0809.2949 “Two-particle”: • v2{2}: each particle with every other particle • v2{subEP}: each particle with the EP of the other subevent • v2{EP} “standard”: each particle with the EP of all the others • v2{SP}: same, weighted with the length of the Q vector Many-particle: • v2{4}: 4-particle - 2 * (2-particle)2 • v2{q}: distribution of the length of the Q vector • v2{LYZ}: Lee-Yang Zeros multi-particle correlation 2-part. methods STAR, J. Adams et al., PRC 72, 014904 (2005) multi-part. methods "Because of nonflow and fluctuations the true v2 lies between the lower band and the mean of the two bands.”

  8. Differences of Measured v2 Values fluctuations nonflow All differences proportional to Without additional assumptions can not separate nonflow and fluctuations

  9. Data Corrected to <v2> corrected to PP published agreement for mean v2 in participant plane

  10. v2 in the Reaction Plane corrected to RP in Gaussian fluctuation approximation: a v2 for theorists Voloshin, Poskanzer, Tang, and Wang, Phys. Lett. B 659, 537 (2008)

  11. Patricia Fachini for the STAR collaboration ρ0 Production in Cu+Cu Collisions at √sNN = 200 and 62.4 GeV in STAR Motivation Measurements Results Conclusions 11 QM2009, Knoxville, March 30 - April 4 Patricia Fachini

  12. Elliptic Flow • Significant ρ0v2 measured  pT > 1.2 GeV/c  v2 ~ 13 ± 4%. 12 QM2009, Knoxville, March 30 - April 4 Patricia Fachini

  13. Elliptic Flow n=4 n=2 • Resonance v2 ρ0(770) production mechanism  scale NCQ  v2/n • ππρ0  n = 4 orqq ρ0  n = 2 • a, b, c, and d constants extracted using KS0and Λ v2ρ0 v2n= 4.7 ± 2.9 • pT range covered not sufficient for conclusive statement on the ρ0production mechanism. X. Dong et al., Phys.Lett. B597 (2004) 328 an v2(pT,n) = - dn 1 + exp[-(pT/n – b)/c] 13 QM2009, Knoxville, March 30 - April 4 Patricia Fachini

  14. Differential Measurements of Hexadecapole (V4) and Elliptic ( V2) Flow as a Probe for Thermalization at RHIC-PHENIX Arkadij Taranenko Nuclear Chemistry Group Stony Brook University for the PHENIX Collaboration

  15. KET and CQN Scaling for v4 V4/(nq)2 vs KET /nq scaling observed for V4 Arkadij Taranenko, QM2009 2020/1/6 15

  16. v4/(v2)2 ratio for different particle species V4 = k(V2)2 where k is the same for different particle species 16

  17. Flow is universal? PHENIX Preliminary Baryon and meson V2 & V4 scale to a universal curve as a function of (KET)/nq Arkadij Taranenko, QM2009 2020/1/6 17

  18. Good fits to the v2 & v4 of charged hadrons Two fit parameters: v2hd and b (a is fixed) ε – participant eccentricity from Glauber Model → PHENIX Preliminary Model ansatz extended from v2 to v4. Good fits obtained both for scaled v2 and v4 .What about fits for PID? 18

  19. Event Anisotropy v2 at STARParticle type, Beam energy and Centrality dependence ShuSu Shi for the STAR collaboration Nuclear Science Division, Lawrence Berkeley National Laboratory Institute of Particle Physics, Central China Normal University

  20. Test Hydro in Small System Ideal hydro: P. Huovinen, private communication • pT < 2 GeV/c • Smaller v2 for heavier hadrons as expected from hydrodynamics. • Sizable v2(Ξ) even in small system • Ideal hydro fails to reproduce the data • Fluctuation of v2? • Viscosity ? • Incomplete thermalization ? STAR preliminary

  21. Energy Dependence • v2 in Cu + Cu (Au +Au) at 200 and 62.4 GeV are comparable within statistical errors STAR preliminary v2 at Cu + Cu 62.4 GeV ~ 12.5 M events - Same procedure used for 200 GeV. - Event plane resolution is 0.088 ± 0.004 in 0 - 60 %, about factor 2 smaller than that in 200 GeV due to lower multiplicity. STAR Au + Au 200 GeV : PRC77, 054901 (2008) Au + Au 62.4 GeV : PRC75, 054906 (2007)

  22. System Size Dependence STAR preliminary Au + Au at 200 GeV • v2 scaled by eccentricity • Remove the initial geometry effect • v2 seems solely depending on initial geometry and number of participant in 200 GeV collisions • v2∝ v2(ε, Npart) Au + Au : PRC77, 054901 (2008) Does v2 in most central reach ideal hydrodynamic limit ?

  23. Ideal Hydro Limit STAR preliminary STAR preliminary Hydro limit ΞΛp K h STAR preliminary • Ideal Hydro Limit • Even in central Au + Au collisions, fitting results indicate that the system is still away from hydro limit v2/ε scaling: S. Voloshin (for STAR Collaboration), J.Phys.G34(2007)S883 PHENIX π, K and p: nucl-ex/0604011v1 CGC eccentricity: H.J. Drescher and Y. Nara, PRC 76 041903 (2007), H.J. Drescher and Y.Nara, PRC 75 034905 (2007)

  24. Effectiveη/s Extracted from Model STAR preliminary • Data shows particle type dependence, not a built-in feature in the model • Can viscous hydrodynamics explain the particle type dependence ? • Inferred η/s depends strongly on the eccentricity model Caveats: Transport model motivated ~ best for dilute system of massless particles no phase transition T: π spectra slope 200 MeV R: Glauber or CGC calculation H. J. Drescher et al, PRC 76 024905 (2007)

  25. The World Collection of η/s STAR preliminary See M. Sharma’s talk for pT correlation

  26. Viscous hydrodynamics with shear and bulk viscosity Huichao Song and Ulrich Heinz The Ohio State University Supported by DOE Quark Matter 2009 March 30-April 4, Knoxville, TN 04/02/2009

  27. Glauber Luzum & Romatschke, PRC 2008 CGC -Glauber vs.CGC ~100% effect on the extracted value of -A detailed extraction of shear viscosity entropy ratio also requires: -viscous late hadronic stage has been studied in ideal hydro -non-equilibrium chemistry in HG -bulk viscosity ? 5 -Present conservative upper limit:

  28. Viscous hydro with shear & bulk viscosity shear viscosity bulk viscosity Conservation laws: Evolution equations for shear pressure tensor and bulk presurre: (2nd order shear-bulk -mixing term (Muronga, Rischke) not included.)

  29. Shear viscosity vs. bulk viscosity (I) Same initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only Local temperature -Shear viscosity:decelerate cooling process in early stage accelerate cooling process in middle and late stages -Bulk viscosity: deceleratecooling process

  30. Shear viscosity vs. bulk viscosity (II) Same Initial & final conditions ideal hydro viscous hydro-shear only viscous hydro-bulk only radial flow spectra -shear viscosity: increases radial flow, results in flatter spectra -bulk viscosity: decreases radial flow, results in steeper spectra

  31. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected

  32. Viscous v2 suppression: shearandbulk viscosity ideal hydro visc. hydro: 30% 20% -at RHIC, 2 x min. bulk viscositycould result in ~50% additional v2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected (a) Change the flow profile during hydro evolution bulk viscosity effects: (b) Additional spectra correction along freeze-out surface Song & Heinz: v2 will decrease, flow corrections only (a),, at freeze-out Monnai & Hirano: v2 will increase,spectra corrections only(b), ideal hydro for evolution

  33. Effects from initialization of (III) Smaller vs.largerrelaxation time -viscous effects from bulk viscosity strongly depend on relaxation time and the initialization for bulk pressure

  34. A Short Summary -first attempts to constrain from RHIC data indicate No consistent simultaneous treatment yet of: a realistic EOS, initialization, bulk viscosity, highly viscous hadronic stage -When extracting QGP viscosity from experimental data, bulk viscosity effects should not be neglected -More theoretical inputs are needed for bulk viscosity: - relaxation time - initialization for bulk pressure - bulk viscosity of hadronic phase, etc

  35. Effects of Bulk Viscosity on pT-Spectra and Elliptic Flow Parameter Akihiko Monnai Department of Physics, The University of Tokyo, Japan Collaborator: Tetsufumi Hirano Quark Matter 2009 March 30th- April 4th, 2009, Knoxville, TN, U.S.A. arXiv:0903.4436 [nucl-th]

  36. Introduction (II) Effects of Bulk Viscosity on pT-spectra and Elliptic Flow Parameter Quark Matter 2009, Knoxville, Tennessee, April 2nd 2009 Cooper & Frye (‘74) freezeout hypersurface Σ particles hadron resonance gas QGP variation of the flow modification of the distribution We estimate this for a multi-component gas. (3+1)-D viscous hydro required. * :normal vector to the freezeout hypersurface element, :distribution of the ith particle, :degeneracy. • Hydrodynamic analyses needs the Cooper-Frye formula at freezeout (i) for comparison with experimental data, (ii) as an interface to a cascade model. • Viscous corrections come in two ways: Introduction (I) Introduction (II) Relativistic Kinetic Theory In Multi-Component System

  37. pT-Spectra Effects of Bulk Viscosity on pT-spectra and Elliptic Flow Parameter Quark Matter 2009, Knoxville, Tennessee, April 2nd 2009 Model of the bulk pressure: : free parameter The bulk viscosity lowers <pT> of the particle spectra. • Au+Au, , b = 7.2(fm), pT -spectra of EoS, Transport Coefficients and Flow pT-Spectra Elliptic Flow Coefficient v2(pT) Results with Quadratic Ansatz

  38. Elliptic Flow Coefficient v2(pT) Effects of Bulk Viscosity on pT-spectra and Elliptic Flow Parameter Quark Matter 2009, Knoxville, Tennessee, April 2nd 2009 The bulk viscosity enhances v2(pT). *Viscous effects might be overestimated for: (1) No relaxation for is from the Navier-Stokes limit. (2) Derivatives of are larger than those of real viscous flow • Au+Au, , b = 7.2(fm), v2(pT) of pT-Spectra Elliptic Flow Coefficient v2(pT) Results with Quadratic Ansatz Summary

  39. A Transport Calculation with an Embedded (3+1)d Hydrodynamic Evolution:Elliptic Flow Results from Elab=2-160 AGeV Quark Matter 2009, 31.03.09, Knoxville, Tennessee Hannah Petersen, Universität Frankfurt Thanks to: Jan Steinheimer, Michael Mitrovski, Gerhard Burau, Qingfeng Li, Gunnar Gräf, Marcus Bleicher, Horst Stöcker, Dirk Rischke (H.P. et al., PRC 78:044901, 2008, arXiv: 0806.1695) (H.P. et al., arXiv: 0901.3821, PRC in print)

  40. Initial State • Contracted nuclei have passed through each other • Energy is deposited • Baryon currents have separated • Energy-, momentum- and baryon number densities are mapped onto the hydro grid • Event-by-event fluctuations are taken into account • Spectators are propagated separately in the cascade (nucl-th/0607018, nucl-th/0511021) Elab=40 AGeV b=0 fm (J.Steinheimer et al., PRC 77,034901,2008)

  41. (3+1)d Hydrodynamic Evolution Ideal relativistic one fluid dynamics employing: • HG: Hadron gas including the same degrees of freedom as in UrQMD (all hadrons with masses up to 2.2 GeV) • CH: Chiral EoS from SU(3) hadronic Lagrangian with first order transition and critical endpoint • BM: Bag Model EoS with a strong first order phase transition between QGP and hadronic phase D. Rischke et al., NPA 595, 346, 1995, D. Rischke et al., NPA 595, 383, 1995 Papazoglou et al., PRC 59, 411, 1999

  42. Freeze-out Chemical FO by Cleymans et al. • Transition from hydro to transport when e < 730 MeV/fm³ (≈ 5 * e0) in all cells of one transverse slice (Gradual freeze-out, GF) iso-eigentime criterion • Transition when e < 5* e0 in all cells(Isochronuous freeze-out, IF) • Particle distributions are generated according to theCooper-Frye formula • with boosted Fermi or Bose distributions f(x,p) including mB and mS • Rescatterings and final decays calculated via hadronic cascade (UrQMD)

  43. Initial State for Non-Central Collisions Pb+Pb at Elab=40 AGeV with b= 7fm at tstart=2.83 fm Energy density profile Weighted velocity profile GeV/fm3 GeV/fm3 Event-by-event fluctuations are taken into account (H.P. et.al., arXiv:0901.3821, PRC in print)

  44. Elliptic Flow • Smaller mean free path in the hot and dense phase leads to higher elliptic flow • At lower energies: hybrid approach reproduces the pure UrQMD result • Gradual freeze-out leads to a better description of the data (H.P. et.al., arXiv:0901.3821, PRC in print) Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star

  45. v2/e Scaling • More realistic initial conditions and freeze-out Qualitative behaviour nicely reproduced • Uncertainty due to eccentricity calculation • Uniqueness of the hydro limit is questioned (H.P. et.al., arXiv:0901.3821, PRC in print) Data and hydro limits from NA49 collaboration, PRC 68, 034903, 2003

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