1. Hydrodynamic Analysis of Relativistic Heavy Ion Collisions at RHIC and LHC Tetsufumi Hirano The Univ. of Tokyo & LBNL Collaborators: Pasi Huovinen and Yasushi Nara Prepared for invited review paper in Progress in Particle and Nuclear Physics Heavy Ion Tea, LBNL, Oct.11, 2010

2. Activities in the Univ. of Tokyo since 2006, stimulated by HIT

3. Outline Introduction Introduction Some highlights from the hybrid model Some highlights from the hybrid model Model: QGP fluid + hadronic cascade picture Model: QGP fluid + hadronic cascade picture Results at RHIC: Results at RHIC: v 2 v 2 source function source function Prediction at RHIC and LHC: Prediction at RHIC and LHC: v 2 in U+U collisions v 2 in U+U collisions v 2 in Pb+Pb collisions v 2 in Pb+Pb collisions Summary Summary

4. Introduction Main aim: Understanding RHIC data based on a systematic analysis with QGP perfect fluid picture Main aim: Understanding RHIC data based on a systematic analysis with QGP perfect fluid picture After press release of perfect fluid discovery in 2005  Much progress: hadronic dissipation, eccentricity fluctuation, lattice EoS, CGC initial condition… After press release of perfect fluid discovery in 2005  Much progress: hadronic dissipation, eccentricity fluctuation, lattice EoS, CGC initial condition… Set a baseline for viscous hydro calculations Set a baseline for viscous hydro calculations Prediction for U+U at RHIC and Pb+Pb at LHC Prediction for U+U at RHIC and Pb+Pb at LHC

5. Ollitrault (’92) Hydro behavior Spatial Anisotropy Momentum Anisotropy INPUT OUTPUT Interaction among produced particles dN/d   No secondary interaction 0 22 dN/d   0 22 2v22v2 x y  Elliptic Flow How does the system respond to spatial anisotropy?

6. Importance of Hadronic Dissipation QGP only QGP+hadron fluids QGP fluid+hadron gas Suppression in forward and backward rapidity Importance of hadronic viscosity TH et al.,(’05)

7. Mass Splitting = Hadronic effects Mass dependence is o.k. from hydro+cascade. When mass splitting appears? 20-30% Proton Pion Mass ordering comes from hadronic rescattering effect. Interplay btw. radial and elliptic flows. TH et al.,(’08)

8. Violation of Mass Splitting Au+Au 200 GeV b=7.2fm TH et al.,(’08)

9. Model No single model to understand heavy ion collision as a whole. No single model to understand heavy ion collision as a whole. Idea: Employ “cutting edge” modules as far as possible Idea: Employ “cutting edge” modules as far as possible 3D ideal hydro 3D ideal hydro Hadronic transport model, JAM Hadronic transport model, JAM Lattice EoS + resonance gas in JAM Lattice EoS + resonance gas in JAM Monte Carlo Glauber/KLN for initial condition Monte Carlo Glauber/KLN for initial condition

10. A Hybrid Approach: Initial Condition 0 collision axis time AuAu QGP fluid hadron gas Model* MC-Glauber MC-KLN (CGC)  part,  R.P. Centrality cut 0-10% 10-20%20-30% … *H.J.Drescher and Y.Nara (2007)

11. Initial Condition w.r.t. Participant Plane Shift: (, ) Rotation:  Throw a dice to choose b and calculate N part average over events average E.g.) N part min = 279 N part max = 394 in Au+Au collisions at 0-10% centrality Participant plane Reaction plane

12.  part and  R.P. Au+AuCu+Cu Eccentricity enhanced due to fluctuationEccentricity enhanced due to fluctuation Significant in small system, e.g., Cu+Cu, perpheal Au+AuSignificant in small system, e.g., Cu+Cu, perpheal Au+Au MC-KLN > MC-Glauber *MC-KLN > MC-Glauber * *See, Drescher and Nara, PRC 75, 034905 (2007).

13. A Hybrid Approach: Hydrodynamics 0 collision axis time AuAu QGP fluid hadron gas Ideal Hydrodynamics # Initial time 0.6 fm/c Lattice + HRG EoS* # Hirano (2002),*Huovinen and Petreczky (2010) + JAM HRG

14. A Hybrid Approach: Hadronic Cascade 0 collision axis time AuAu QGP fluid hadron gas Interface Cooper-Frye formula at switching temperature T sw = 155 MeV Hadronic afterburner Hadronic transport model based on kinetic theory  JAM* *Y.Nara et al., (2000)

15. Comparison of Hydro+Cascade Results with Available Data

16. p T Spectra: MC-Glauber Filled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascade From top to bottom, 0-5, 5-10, 10-15, …, 70-80% centrality (1) Absolute value of entropy, (2) soft/hard fraction  = 0.18, and (3) switching temperature T sw = 155 MeV.

17. p T Spectra: MC-KLN (1) Absolute value of saturation scale and (2) scaling parameters =0.28 and (3) switching temperature T sw = 155 MeV Filled: PHENIX, PRC69, 034909 (2004), Open: Hydro+cascade From top to bottom, 0-5, 5-10, 10-15, …, 70-80% centrality

18. v 2 (N part ) Au+AuCu+Cu MC-Glauber: Apparent reproduction. No room for QGP viscosity? MC-KLN: Overshoot due to larger eccentricity. How small QGP viscosity? p T >0 PHOBOS, PRC72, 051901 (2005); PRL98, 242302 (2007).

19. v 2 (centrality) Au+AuCu+Cu p T cut enhances v 2 by ~10%p T cut enhances v 2 by ~10% STAR data in Au+Au corrected by Ollitrault et al.*STAR data in Au+Au corrected by Ollitrault et al.* v 2 w.r.t. participant planev 2 w.r.t. participant plane 0.15 < p T < 2 GeV/c *J.Y.Ollitrault, A.M.Poskanzer and S.A.Voloshin, PRC80, 014904 (2009).

20. v 2 (p T ) for PID Particles Results based on MC-Results based on MC- Glauber initialization Mass splitting pattern OKMass splitting pattern OK A little bit overshoot evenA little bit overshoot even in low p T region  Centrality dependence (next slide)? PHENIX, PRL91, 182301 (2003) 0-80%

21. v 2 (p T ) for PID Particles: Centrality Dependence 0-20% 20-40% 40-60% Hydro+cascade withHydro+cascade with MC-Glauber at work in 0-20% centrality Need QGP viscosityNeed QGP viscosity Or, need jet orOr, need jet orrecombination/coalescencecomponents? MC-KLN results not availableMC-KLN results not available yet due to less statistics PHENIX, PRL91, 182301 (2003)

22. v 2 (p T ) for Charged Particles: Au+Au Hydro+cascade with MC-Glauber at work in low p THydro+cascade with MC-Glauber at work in low p T p T region at work shrinks as moving to peripheralp T region at work shrinks as moving to peripheral  Importance of viscosity PHENIX, PRC80, 024909 (2009). STAR, PRC72, 014904 (2005).

23. v 2 (p T ) for Charged Particles: Cu+Cu Tendency is the same as that in Au+Au collisionsTendency is the same as that in Au+Au collisions PHENIX, PRL98, 162301 (2007). STAR, PRC81, 044902 (2010).

24. v 2 (p T ) for Charged Particles: Au+Au Hydro+cascade with MC-KLN at workHydro+cascade with MC-KLN at work in central collisions PHENIX, PRC80, 024909 (2009). STAR, PRC72, 014904 (2005).

25. MC-KLN vs. MC-Glauber Slope of v 2 (p T ) steeper in MC-KLN than in MC-Glauber  v 2,MC-KLN > v 2,MC-Glauber p T dependent viscousp T dependent viscous correction at T=T sw might interpret the data Extracted transportExtracted transport coefficients depend on initial condition

26. Conventional Femtoscopic Analysis Particle source Detector 1 Detector 2 Hanbury Brown – Twiss (1956) Goldhaber – Goldhaber – Lee – Pais (1960) Source size of particle emission (Homogeneity region)  Information in configuration space

28. New Technique: Source Imaging Koonin-Pratt eq.: Inverse problem Source function and emission rate: Primed (‘) variables in Pair Center-of-Mass System Brown, Danielewicz(1997)

29. 1D Source Function for Pions With hadronic rescattering and decays Without hadronic rescattering and decays Non-Gaussian tail in pion source function from hybrid model Au+Au, 0-30% 0.3 < k T < 0.9 GeV/c Au+Au, 0-30% 0.3 < k T < 0.9 GeV/c PHENIX, PRL103, 142301(2009)

30. 1D Source Function for Kaons With hadronic rescattering and decays Without hadronic rescattering and decays Non-Gaussian tail in kaon source function from hybrid model Au+Au, 0-30% 0.3 < k T < 0.9 GeV/c Au+Au, 0-30% 0.3 < k T < 0.9 GeV/c PHENIX, PRL103, 142301(2009)

31. Emission Rate for Pions 0-30% Au+Au, pions, 0.3 < p x < 0.9 GeV/c Without hadronic rescattering or decays  Negative x-t correlation

32. Emission Rate for Pions 0-30% Au+Au, pions, 0.3 < p x < 0.9 GeV/c With hadronic rescattering and decays  Positive x-t correlation(?)

33. Emission Rate for Kaons 0-30% Au+Au, kaons, 0.3 < p x < 0.9 GeV/c Without hadronic rescattering or decays  Negative x-t correlation

34. Emission Rate for Kaons 0-30% Au+Au, kaons, 0.3 < p x < 0.9 GeV/c With hadronic rescattering and decays  Positive x-t correlation(?)

35. Predictions from Hydro+Cascade Model

36. Collisions of Deformed Nuclei at RHIC How v 2 /  behaves asHow v 2 /  behaves as increasing multiplicity?* Saturate?Saturate? Still enhance?Still enhance? U+U collision in run12 at RHIC(?) More multiplicityMore multiplicity Larger eccentricityLarger eccentricity STAR, PRC66, 034904 (2002) *U.Heinz and A. Kuhlman, PRL94, 132301 (2005).

37. Eccentricity in U+U Collisions at RHIC Larger eccentricityLarger eccentricity Finite eccentricity atFinite eccentricity at zero impact parameter body-body collision Unable to controlUnable to control configuration  Need Monte-Carlo study and event selection* *See, e.g., P.Filip et al. PRC80, 054903 (2009). 0-5%  0.146 (MC-Glauber), 0.148 (MC-KLN)

38. v 2 in U+U Collisions v 2 increases due to deformation of colliding nuclei.v 2 increases due to deformation of colliding nuclei. v 2 /  scales with transverse density.v 2 /  scales with transverse density. Maximum transverse density increases only by ~10%Maximum transverse density increases only by ~10% in central U+U collisions.

39. Prediction at LHC Eccentricity does not change from RHIC to LHC! Change due solely to size v 2 /  does not follow RHIC scaling curve

40. v 2 /  Scales at Fixed Collision Energy Increase multiplicity with fixed centrality. Pick up points with fixed centrality consistent P.F.Kolb et al., PRC62, 054909 (2000)

41. Summary Current status of the hybrid approach Current status of the hybrid approach Elliptic flow Elliptic flow MC-Glauber initialization gives a reasonable agreement with data in very central collisions. MC-Glauber initialization gives a reasonable agreement with data in very central collisions. Results deviate from data as moving away from central collisions. Results deviate from data as moving away from central collisions. QGP viscosity? QGP viscosity? Source function Source function Non-Gaussian tail is seen through hadronic rescatterings and decays Non-Gaussian tail is seen through hadronic rescatterings and decays Prediction Prediction Results in U+U collisions follow scaling behavior, extend (1/S)dN ch /d  by ~10% Results in U+U collisions follow scaling behavior, extend (1/S)dN ch /d  by ~10% v 2 /  at LHC does not follow scaling seen at RHIC v 2 /  at LHC does not follow scaling seen at RHIC

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44. p T Spectra in STAR and PHENIX Central: Consistent btw. STAR and PHENIX Peripheral: (STAR) > (PHENIX) STAR data are 50 % larger than PHENIX data STAR, PRC 79, 034909 (2009) PHENIX, PRC69, 034909 (2004)

45. Steeper Transverse Profile in CGC Closer to hard sphere than Glauber Note: Original KLN model (not fKLN)

46. Event Distributions from Monte Carlo Centrality cut is done according to N part

47. Correlation btw. N part and N coll Au+AuU+U N part N coll

48. 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

49. Event-by-Event Eccentricity

50. Normalization in Source Function Source function multiplied by phase space density

51. Comparison of Source Functions Both normalized to be unity

52. Normalization in PHENIX??? (fm -2 )