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) 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 S. Pratt, arXiv: v1

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

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

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

8 Differences of Measured v 2 Values All differences proportional to Without additional assumptions can not separate nonflow and fluctuations nonflow fluctuations

9 Data Corrected to published agreement for mean v 2 in participant plane corrected to PP

10 corrected to RP v 2 in the Reaction Plane in Gaussian fluctuation approximation: Voloshin, Poskanzer, Tang, and Wang, Phys. Lett. B 659, 537 (2008) a v 2 for theorists

11 QM2009, Knoxville, March 30 - April 4 Patricia Fachini 11 Patricia Fachini for the STAR collaboration Motivation Measurements Results Conclusions ρ 0 Production in Cu+Cu Collisions at √s NN = 200 and 62.4 GeV in STAR

12 Significant ρ 0 v 2 measured  p T > 1.2 GeV/c  v 2 ~ 13 ± 4%. Elliptic Flow 12 QM2009, Knoxville, March 30 - April 4 Patricia Fachini

13 QM2009, Knoxville, March 30 - April 4 Patricia Fachini 13 Elliptic Flow Resonance v 2  ρ 0 (770) production mechanism  scale NCQ  v 2 /n ππ  ρ 0  n = 4 or qq  ρ 0  n = 2 a, b, c, and d  constants extracted using K S 0 and Λ v 2 ρ 0  v 2  n= 4.7 ± 2.9  p T range covered not sufficient for conclusive statement on the ρ 0 production mechanism. v 2 (p T,n) = - dn 1 + exp[-(p T /n – b)/c] anan X. Dong et al., Phys.Lett. B597 (2004) 328 n=2 n=4

14 Differential Measurements of Hexadecapole (V 4 ) and Elliptic ( V 2 ) Flow as a Probe for Thermalization at RHIC- PHENIX Arkadij Taranenko Nuclear Chemistry Group Stony Brook University for the PHENIX Collaboration

Arkadij Taranenko, QM KE T and CQN Scaling for v 4 V 4 /(n q ) 2 vs K ET /n q scaling observed for V 4

16 V 4 = k(V 2 ) 2 where k is the same for different particle species v 4 /(v 2 ) 2 ratio for different particle species

Arkadij Taranenko, QM Baryon and meson V 2 & V 4 scale to a universal curve as a function of (KE T )/n q PHENIX Preliminary Flow is universal?

18 PHENIX Preliminary Good fits to the v 2 & v 4 of charged hadrons Good fits to the v 2 & v 4 of charged hadrons Model ansatz extended from v 2 to v 4. Good fits obtained both for scaled v 2 and v 4. What about fits for PID? Two fit parameters: v 2 hd and  (  is fixed) → ε – participant eccentricity from Glauber Model

19 Event Anisotropy v 2 at STAR Particle 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 p T < 2 GeV/c  Smaller v 2 for heavier hadrons as expected from hydrodynamics. Sizable v 2 (Ξ) even in small system Ideal hydro fails to reproduce the data  Fluctuation of v 2 ?  Viscosity ?  Incomplete thermalization ? STAR preliminary

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

22 STAR preliminary Au + Au at 200 GeV Au + Au : PRC77, (2008) System Size Dependence Does v 2 in most central reach ideal hydrodynamic limit ? v 2 scaled by eccentricity  Remove the initial geometry effect v 2 seems solely depending on initial geometry and number of participant in 200 GeV collisions  v 2 ∝ v 2 (ε, N part )

23 STAR preliminary v 2 /ε scaling: S. Voloshin (for STAR Collaboration), J.Phys.G34(2007)S883 PHENIX π, K and p: nucl-ex/ v1 CGC eccentricity: H.J. Drescher and Y. Nara, PRC (2007), H.J. Drescher and Y.Nara, PRC (2007) Ideal Hydro Limit STAR preliminary Hydro limit ΞΛ p 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

24 Effectiveη /s Extracted from Model Caveats: Transport model motivated ~ best for dilute system of massless particles no phase transition 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 T: π spectra slope 200 MeV R: Glauber or CGC calculation H. J. Drescher et al, PRC (2007)

25 The World Collection of η /s STAR preliminary See M. Sharma ’s talk for p T correlation

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

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

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

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

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

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

37 Viscous v2 suppression: shear and bulk viscosity ideal hydro visc. hydro: -at RHIC, 2 x min. bulk viscosity could result in ~50% additional v 2 suppression -when extracting the from RHIC data, bulk viscous effects cannot be neglected 20% 30% bulk viscosity effects: (a) Change the flow profile during hydro evolution (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

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

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

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

41 Introduction (II) 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: (3+1)-D viscous hydro required. We estimate this for a multi-component gas. Cooper & Frye (‘74) Quark Matter 2009, Knoxville, Tennessee, April 2 nd 2009 Effects of Bulk Viscosity on p T -spectra and Elliptic Flow Parameter Introduction (II) Introduction (I) Relativistic Kinetic Theory variation of the flowmodification of the distribution * :normal vector to the freezeout hypersurface element, :distribution of the i th particle, :degeneracy. particles hadron resonance gas QGP freezeout hypersurface Σ In Multi-Component System

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

43 Elliptic Flow Coefficient v 2 (p T ) Au+Au,, b = 7.2(fm), v 2 (p T ) of The bulk viscosity enhances v 2 (p T ). *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 Summary Results with Quadratic Ansatz Quark Matter 2009, Knoxville, Tennessee, April 2 nd 2009 Effects of Bulk Viscosity on p T -spectra and Elliptic Flow Parameter p T -Spectra Elliptic Flow Coefficient v 2 (p T )

44 A Transport Calculation with an Embedded (3+1)d Hydrodynamic Evolution: Elliptic Flow Results from E lab =2-160 AGeV Quark Matter 2009, , 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: ) (H.P. et al., arXiv: , PRC in print)

45 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 (J.Steinheimer et al., PRC 77,034901,2008) (nucl-th/ , nucl-th/ ) E lab =40 AGeV b=0 fm

46 (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

47 Freeze-out 1)Transition from hydro to transport when  < 730 MeV/fm³ (≈ 5 *  0 ) in all cells of one transverse slice (Gradual freeze-out, GF)  iso-eigentime criterion 2)Transition when  < 5*  0 in all cells (Isochronuous freeze-out, IF) Particle distributions are generated according to the Cooper-Frye formula with boosted Fermi or Bose distributions f(x,p) including m B and m S Rescatterings and final decays calculated via hadronic cascade (UrQMD) Chemical FO by Cleymans et al.

48 Initial State for Non-Central Collisions Pb+Pb at E lab =40 AGeV with b= 7fm at t start =2.83 fm Energy density profileWeighted velocity profile  Event-by-event fluctuations are taken into account (H.P. et.al., arXiv: , PRC in print) GeV/fm 3

49 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: , PRC in print) Data from E895, E877, NA49, Ceres, Phenix, Phobos, Star

50 v 2 /  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: , PRC in print) Data and hydro limits from NA49 collaboration, PRC 68, , 2003

51 Eccentricity fluctuation of initial conditions in hydrodynamics Tetsufumi Hirano Department of Physics Graduate School of Science The University of Tokyo Quark Matter 2009 Collaborator: Yasushi Nara (Akita Intl. Univ.)

52 Eccentricity Fluctuation Interaction points of participants vary event by event.  Apparent reaction plane also varies.  The effect is significant for smaller system such as Cu+Cu collisions Adopted from D.Hofman(PHOBOS), talk at QM2006 A sample event from Monte Carlo Glauber model ii 00

53 Initial Condition with an Effect of Eccentricity Fluctuation Rotate each  i to  true Throw a dice to choose b: b min <b<b max average over events average E.g.) b min = 0.0fm b max = 3.3fm in Au+Au collisions at 0-5% centrality With fluctuation effects Without fluctuation effects

54 Inputs in Model Calculations Parameters are fixed in Au+Au collisions Glauber: KLN: standard parameters KLN: Kharzeev-Levin-Nardi model

55 Eccentricity with Fluctuation EffectsAu+Au Cu+Cu Large fluctuation in small system such as Cu+Cu and peripheral Au+Au

56 Centrality Dependence (Glauber)Au+Au Cu+Cu Large fluctuation effects in Cu+Cu collisions Cu+Cu data also constrain the models Glauber initialization undershoots data!?

57 Centrality Dependence (KLN) Large fluctuation effects again in Cu+Cu collisions Reasonable agreement btw. data and MC-KLN!? Au+Au Cu+Cu

58 Backup slides

59 HBT nomenclature x Actual q distribution Background q distribution = The source S can be directly recovered with imaging Make assumptions about the source adapted from Annu. Rev. Nucl. Part. Sci : Detector Simplified for identical particles or Bose-Einstein Enhancement at Low q

60 Include Fluctuations in absence of fluctuations for full events, it is more complicated

61 PHOBOS+  Equation for Subevents Eq. Fluctuations! I 0,1 are modified Bessel functions resolution parameter only function of 

62 Analytic Correction for Fluctuations method similar to momentum conservation correction: N. Borghini, P.M. Dinh, J.-Y. Ollitrault, A.M. Poskanzer, and S.A. Voloshin, PRC 66, (2002)

63 Analytic Correction for Nonflow nonflow

64 v 2 Fluctuations from  part Fluctuations Assume width with same percent width as  part : 2D Gaussian fluctuations in reaction plane lead to Bessel-Gaussian fluctuations along the participant plane axis   is from standard deviation of nucleon MC Glauber of  part Bessel-Gaussian: Voloshin et al., Phys. Lett. B 659, 537 (2008)

65 Assumptions Application to Data MC Glauber  participant less nonflow

66 Nonflow and Fluctuations with my assumptions and parameters:

67 K 0 =0.7 (from transport calculation) c s = speed of sound [fixed]  = eccentricity S = transverse nuclear overlap area dN/dy – total multiplicity per unit rapidity C.Gombeaud and J-Y.Ollitrault; Phys. Rev. C 77, (2008) Hydro description: –Ideal hydro: scale invariance leads to eccentricity scaling v2/ε ~ const –Real (viscous) hydro: Eccentricity scaling is broken and v2/ε !=const Transport description (Ollitrault): –Operational Ansatz: The Boltzmann equation reduces to hydrodynamics when the mean free path is small –v2/ε is a function of the Knudsen number K n = λ / R : [ R – transverse size of the system and λ is the mean free path ] K n →0 (ideal hydro limit) : v 2 /ε ~ constant K n >>1 (low density limit) : v 2 /ε ~ v 2 hd / (ε K n / K 0 ) 67 C. Marle, Annales Poincare Phys.Theor. 10,67 (1969). 2 free parameters in the fit  = effective partonic cross section (4~6mb) v 2 hd = hydrodynamic limit Extraction of transport coefficients PHOBOS data,  s=200 GeV H-J.Drescher, A.Dumitru, C.Gombeaud, J- Y.Ollitrault; Phys. Rev. C 76, (2007)

68 H. Song, U. W. Heinz Phys.Rev.C78:024902,2008 Operational test of hydro calculation

69 Results with Quadratic Ansatz p T -spectra and v 2 (p T ) of with and the same EoS Results with Quadratic Ansatz Summary Quark Matter 2009, Knoxville, Tennessee, April 2 nd 2009 Effects of Bulk Viscosity on p T -spectra and Elliptic Flow Parameter Effects of the bulk viscosity is underestimated in quadratic ansatz. Elliptic Flow Coefficient v 2 (p T )

70 Summary & Outlook Consistent determination of for a multi-particle system A non-zero trace tensor term is needed for the hadron resonance gas up to the mass of Visible effects of on particle spectra Bulk viscosity should be considered to constrain the transport coefficients with better accuracy from experimental data. A (3+1)-dimensional viscous hydrodynamic flow is necessary to see more realistic behavior of the particle spectra. Summary Results with Quadratic Ansatz Quark Matter 2009, Knoxville, Tennessee, April 2 nd 2009 Effects of Bulk Viscosity on p T -spectra and Elliptic Flow Parameter p T -spectra : suppressed v 2 (p T ) : enhanced when estimated with an ideal hydrodynamic flow.

71 Hybrid Approaches Hadronic freezeout following a first order hadronization phase transition in ultrarelativistic heavy ion collisions. S.A. Bass, A. Dumitru, M. Bleicher, L. Bravina, E. Zabrodin, H. Stoecker, W. Greiner, Phys.Rev.C60:021902,1999 Dynamics of hot bulk QCD matter: From the quark gluon plasma to hadronic freezeout. S.A. Bass, A. Dumitru, Phys.Rev.C61:064909,2000 Flow at the SPS and RHIC as a quark gluon plasma signature. D. Teaney, J. Lauret, Edward V. Shuryak, Phys.Rev.Lett.86: ,2001 A Hydrodynamic description of heavy ion collisions at the SPS and RHIC. D. Teaney, J. Lauret, E.V. Shuryak, e-Print: nucl-th/ Hadronic dissipative effects on elliptic flow in ultrarelativistic heavy-ion collisions. T. Hirano, U. Heinz, D. Kharzeev, R. Lacey, Y. Nara, Phys.Lett.B636: , D hydro + cascade model at RHIC. C. Nonaka, S.A. Bass, Nucl.Phys.A774: ,2006 Results On Transverse Mass Spectra Obtained With Nexspherio F. Grassi, T. Kodama, Y. Hama, J.Phys.G31:S1041-S1044,2005 See also recent work of K. Werner

72 Introduction Fix the initial state and freeze-out  learn something about the EoS and the effect of viscous dynamics 1) Non-equilibrium initial conditions via UrQMD 2) Hydrodynamic evolution or Transport calculation 3) Freeze-out via hadronic cascade (UrQMD) UrQMD-2.3 is available at

73 Transverse Momentum Dependence Hydro phase leads to higher flow values, but weak EoS dependence NA49 (NA49, PRC 68, , 2003) ProtonsPions

74 Conclusions Integrated approach with the same initial conditions and freeze-out for different EoS Particle multiplicities and spectra are reasonably reproduced, strangeness enhanced Transverse momentum spectra indicate importance of non- equilibrium effects Phase transition is visible in HBT radii, but long fireball lifetime so far not supported by the existing data Flow results depend crucially on initial conditions and freeze-out See also Poster 927 by Jan Steinheimer about new chiral EoS including deconfinement phase transition Poster 403 by Björn Bäuchle about direct photons

75 Comment on Monte Carlo Approach How do we consider this? Naïve Glauber calculation: MC-Glauber calculation: Finitenucleonprofile

76 Comment on Monte Carlo Approach (contd.)  Reduction of eccentricity by ~5-10%  Necessity of re-tuning parameters in Woods-Saxon density  We have retuned parameters.

77 Comment on v 2 /  vs. (1/S)dN/dy Hydro limit = (no viscosity) + (small freezeout T)  Ideal hydro of QGP does NOT give a hydro limit curve due to limit curve due tohadronization and finite life time. “hydro limit” Exp. data would reflect life time of the QGP rather than its viscosity.

78 Summary & Outlook Implement of eccentricity fluctuation in hydro initial conditions Large fluctuation effects seen in small system MC-Glauber case –Undershooting the data!? No room for viscosity? MC-KLN case –Reasonable results? Viscosity could play a role? Realistic EOS, viscosity,…