Hydrodynamics in Heavy Ion Collisions and QCD Equation of State

1. Hydrodynamics in Heavy Ion Collisions and QCD Equation of State Current status of a 3D hydro+cascade model Tetsufumi Hirano Department of Physics The University of Tokyo References: T.Hirano, U.W.Heinz, D.Khaezeev, R.Lacey, Y.Nara Phys.Lett.B636, 299 (2006); J.Phys.G34, S879 (2007); arXiv:0710.5795 [nucl-th] (Phys.Rev.C, in press.). T.Hirano, U.Heinz, (work in progress).

2. A Remark at the Beginning Hydrodynamic Model ≠Hydrodynamics So far, discovery of the perfect fluid QGP has been made by one particular modeling of relativistic hydrodynamics. How robust/fragile is the discovery? See, Huovinen’s talk

3. Inputs for Hydrodynamic Simulations for Perfect Fluids Final stage: Free streaming particles  Need decoupling prescription t Intermediate stage: Hydrodynamics can be valid as far as local thermalization is achieved.  Need EOS P(e,n) z 0 • Initial stage: • Particle production, • pre-thermalization? • Instead, initial conditions for hydro simulations

4. Our Strategy:QGP fluid + hadronic cascadein full 3D space • Initial condition: • Glauber model • CGC model • QGP fluid: • 3D ideal hydrodynamics • (Tc = 170 MeV) • 1. massless free u,d,s+g • gas + bag const. • 2. Soft EoS • Hadron phase: • Tth=100MeV • Hadronic cascade • (Tsw = 169 MeV) hadron gas time QGP fluid collision axis 0 Au Au Hybrid approaches: (1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak, (3D) Nonaka, Bass, Hirano et al.

5. Two Hydro Initial Conditions Which Clear the “First Hurdle” Centrality dependence Rapidity dependence 1.Glauber model Npart:Ncoll = 85%:15% 2. CGC model Matching I.C. via e(x,y,hs) Kharzeev, Levin, and Nardi Implemented in hydro by TH and Nara

6. QGP fluid+hadron gas with Glauber I.C. pT Spectra for PID hadrons A hybrid model works well up to pT~1.5GeV/c. Other components (reco/frag) would appear above.

7. QGP+hadron fluids with Glauber I.C. Centrality Dependence of v2 TH et al. (’06) • v2 data are comparable with hydro results. • Hadronic cascade cannot reproduce data. • Note that, in v2 data, there exists eccentricity fluctuation which is not considered in model calculations. hadronic cascade result (Courtesy of M.Isse)

8. QGP+hadron fluids with Glauber I.C. Pseudorapidity Dependence of v2 • v2 data are comparable with hydro results again around h=0 • Not a QGP gas  sQGP • Nevertheless, large discrepancy in forward/backward rapidity QGP+hadron QGP only h<0 h>0 h=0 TH(’02); TH and K.Tsuda(’02); TH et al. (’06).

9. QGP fluid+hadron gas with Glauber I.C. Importance of Hadronic “Corona” QGP fluid+hadron gas • Boltzmann Eq. for hadrons instead of hydrodynamics • Including effective viscosity through finite mean free path QGP+hadron fluids QGP only T.Hirano et al.,Phys.Lett.B636(2006)299.

10. QGP fluid+hadron gas with Glauber I.C. Differential v2, centrality dependence 20-30% • Centrality dependence is ok • Large reduction from pure hydro in small multiplicity events Mass dependence is o.k. Note: First result was obtained by Teaney et al. T.Hirano et al.(’07)

11. QGP fluid+hadron gas with Glauber I.C. Differential v2 in Forward hybrid model AMPT Adopted from S.J.Sanders (BRAHMS) talk @ QM2006

12. QGP fluid+hadron gas with Glauber I.C. Mass Ordering for v2(pT) Pion 20-30% Proton Mass ordering comes from hadronic rescattering effect. Interplay btw. radial and elliptic flows. Mass dependence is o.k. from hydro+cascade.

13. QGP fluid+hadron gas with Glauber I.C. f-meson case Just after hadronization Final results b=7.2fm b=7.2fm T = Tsw = 169 MeV in pT < 1 GeV/c Violation of mass ordering for phi mesons! Clear signal of early decoupling! Caveat: Published PHENIX data obtained in pT>~1GeV/c for f mesons

14. QGP fluid+hadron gas with Glauber I.C. Centrality Dependence of Differential v2 PHENIX PHENIX Pions, AuAu 200 GeV Thanks to M.Shimomura (Tsukuba)

15. QGP fluid+hadron gas with Glauber I.C. Hybrid Model at Work at sqrt(sNN)=62.4 GeV PHENIX PHENIX Pions, AuAu 62.4 GeV Thanks to M.Shimomura (Tsukuba)

16. QGP fluid+hadron gas with Glauber I.C. Differential v2 in Au+Au and Cu+Cu Collisions Au+Au Cu+Cu Same Npart, different eccentricity Au+Au Cu+Cu Same eccentricity, different Npart

17. QGP fluid+hadron gas with Glauber I.C. Distribution of the Last Interaction Point from Hydro + Cascade x-y x-t • px ~ 0.5 GeV/c for pions • Long tail (w decay? elastic scattering?) • Positive x-t correlation Blink: Ideal Hydro, no resonance decays Kolb and Heinz (2003)

18. QGP fluid+hadron gas with Glauber I.C. 1D (Angle-averaged) Source Function from Hydro + Cascade KT=PT/2 0.2 < KT <0.36 GeV/c 0.48 < KT <0.6 GeV/c • Broader than PHENIX data • Almost no KT dependence ?PHENIX data • Significant effects of hadronic rescatterings PHENIX, PRL98,132301(2007); arXiv:0712.4372[nucl-ex]

19. Summary So Far • A hybrid approach (QGP fluid + hadronic cascade) initialized by Glauber model works quite well. • (KT dependence of source size?) • So far, so good. • What happens if initial condition is changed?

20. Eccentricity from CGC Initial Condition y x Hirano et al.(’06). Kuhlman et al.(’06), Drescher et al.(’06). See also, Lappi, Venugopalan (’06) Drescher, Nara (’07)

21. QGP fluid+hadron gas with CGC I.C. v2 Depends on Initialization • Glauber: • Early thermalization • Discovery of Perfect Fluid QGP • CGC: • No perfect fluid? • Additional viscosity • required in QGP? TH et al.(’06) Important to understand initial conditions much better for making a conclusion Adil, Gyulassy, Hirano(’06)

22. QGP fluid+hadron gas with CGC I.C. Soft EoS or Viscosity? v2 is sensitive to sound velocity. Soft EoS in the QGP phase leads to reasonable reproduction of v2  Again, importance of understanding initial conditions. Imprement of Lattice EoS?

23. Summary and Outlook • Success and challenge of a hydro + cascade model • Glauber + hard QGP EoS + hadronic afterburner • CGC + soft QGP EoS + hadronic afterburner • Future studies  Higher Tc, Tsw or Lattice EoS  Fluctuation of initial geometry

24. Why they shift oppositely? pions protons v2(pT) v2 <pT> pT v2 for protons can be negative even in positive elliptic flow must decrease with proper time TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01)

25. What happens to strangeness sector?

26. Distribution of Freeze-Out Time (no decay) b=2.0fm Early kinetic freezeout for multistrange hadrons: van Hecke, Sorge, Xu(’98) Phi can serve a direct information at the hadronization.

27. phi/p Ratio as a function of pT • pp collisions • Pure hydro in AA • collisions • Hydro + cascade • in AA collisions Clear signal for early decoupling of phi mesons

28. Recent Results from Lattice 1 16 81 e (GeV/fm3) Max e0 ~ 45 GeV/fm3 Ave. e0 ~ 13 GeV/fm3 in hydro at RHIC M.Cheng et al., Phys.Rev.D77,014511 (2008).

29. Source Imaging Primed quantities in Pair Co-Moving System (PCMS) (P = 0) Koonin-Pratt eq. (Koonin(’77),Pratt(’84)): Source function and normalized emission rate Source Imaging: Inverse problem from C to D with a kernel K No more Gaussian parameterization! (Brown&Danielewicz (’97-))

30. Long Tail Attributable to w Decay ? No! Switch off omega decay by hand in hadronic cascade  Long tail is still seen.  Soft elastic scattering of pions? b=5.8fm Plot: PHENIX Hist.: Hydro+cascade w/o w decay

31. 3D Source Function from Hydro + Cascade side out long • Source function in PCMS • 1fm-slice in each direction • 0.2<KT<0.4 GeV/c, |h| < 0.35, p+-p+, p--p- pairs • Black: With rescattering, Red: Without rescattering • No longer Gaussian shape (Lines: Gaussian) • Significantly broadened by hadronic rescatterings