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Hydrodynamic Analysis of Heavy Ion Collisions at RHIC

Strangeness in Quark Matter Tsinghua University, Beijing, China October 6-10, 2008. Hydrodynamic Analysis of Heavy Ion Collisions at RHIC. Tetsufumi Hirano Department of Physics The University of Tokyo. “Hydrodynamics and Flow”, T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:0808.2684.

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Hydrodynamic Analysis of Heavy Ion Collisions at RHIC

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  1. Strangeness in Quark Matter Tsinghua University, Beijing, China October 6-10, 2008 Hydrodynamic Analysis of Heavy Ion Collisions at RHIC Tetsufumi Hirano Department of Physics The University of Tokyo “Hydrodynamics and Flow”, T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:0808.2684

  2. Dynamical Modeling with Hydrodynamics Initial condition (thermalization) Recombination Coalescence Information on surface of QGP Hydrodynamic evolution of QGP Information inside QGP Kinetic evolution • Jet quenching/Di-jet • Heavy quark diffusion • J/psi suppression • Electromagnetic radiation • … Hadronic spectra (Collective flow)

  3. QGP fluid + hadronic cascadein full 3D space • Initial condition (t=0.6fm): • Glauber model • CGC model • QGP fluid: • 3D ideal hydrodynamics • (Tc = 170 MeV) • Massless free u,d,s+g • gas + bag const. • Hadron phase: • Tth=100MeV • Hadronic cascade (JAM) • (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.

  4. 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

  5. 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.

  6. 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)

  7. 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).

  8. 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.

  9. 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.

  10. 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.

  11. What happens to strangeness sector?

  12. 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.

  13. 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

  14. QGP fluid+hadron gas with Glauber I.C. Violation of Mass Ordering for f-mesons 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

  15. Eccentricity Fluctuation Adopted from D.Hofman(PHOBOS), talk at QM2006 Yi A sample event from Monte Carlo Glauber model Y0 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

  16. Initial Condition with an Effect of Eccentricity Fluctuation Throw a dice to choose b: bmin<b<bmax average over events Rotate each Yi to Ytrue E.g.) bmin= 0.0fm bmax= 3.3fm in Au+Au collisions at 0-5% centrality average over events

  17. Effect of Eccentricity Fluctuation on v2 v2(w.rot) ~ 2 v2(w.o.rot) at Npart~350 in AuAu v2(w.rot) ~ 4 v2(w.o.rot) at Npart~110 in CuCu Significant effects of fluctuation! Still a lack of flow?  CGC initial conditions?

  18. Summary So Far • A hybrid approach (QGP fluid + hadronic cascade) initialized by Glauber model works reasonably well at RHIC. • Starting point to study finite temperature QCD medium in H.I.C. • More detailed comparison with data is mandatory. (EoS, CGC initial conditions, viscosity, eccentricity fluctuation, …)

  19. Application of Hydro Results Thermal radiation (photon/dilepton) Jet quenching J/psi suppression Heavy quark diffusion Recombination Coalescence Meson J/psi c Baryon c bar Information along a path Information on surface Information inside medium

  20. Talk by T.Gunji, in Parallel 6, 11:15-(Tues.) J/psi Suppression • Quarkonium suppression in QGP • Color Debye Screening • T.Matsui & H. Satz PLB178 416 (1986) • Suppression depends on temperature (density) and radius of QQbar system. • TJ/psi : 1.6Tc~2.0Tc • Tc, Ty’ : ~ 1.1Tc • May serve as the thermometer in the QGP. M.Asakawa and T.Hatsuda, PRL. 92, 012001 (2004) A. Jakovac et al. PRD 75, 014506 (2007) G.Aarts et al. arXiv:0705.2198 [hep-lat]. (Full QCD) See also T.Umeda,PRD75,094502(2007)

  21. Best fit @ (TJ/y, Tc, fFD) = (2.00Tc, 1.34Tc, 10%) T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007; J.Phys.G: Nucl.Part.Phys. 35, 104137 (2008). Results from Hydro+J/psi Model 1s 2s Bar: uncorrelated sys. Bracket: correlated sys. Contour map • Onset of J/y suppression at Npart ~ 160. • ( Highest T at Npart~160 reaches to 2.0Tc.) • Gradual decrease of SJ/ytotabove Npart~160 reflects transverse area with T>TJ/y increases. • TJ/ycan be determined in a narrow region.

  22. Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499. Heavy Quark Diffusion Relativistic Langevin Eq. in local rest frame G: Drag coefficient x: Gaussian white noize Phenomenological parametrization of G T: temperature from hydro sim. M: Mass of c or b quark LOpQCD(PYTHIA)  Langevin sim. in QGP  (Indep.) fragmentation  Semi leptonic Decay

  23. Y.Akamatsu, T.Hatsuda,T.Hirano,arXiv:0809.1499. Results from Langevin Simulations on 3D QGP Hydro g~1-3 from RAA Heavy quarks are not completely thermalized

  24. Application of Hydro Results Thermal radiation (photon/dilepton) Jet quenching J/psi suppression Heavy quark diffusion Recombination Coalescence Meson J/psi c Baryon c bar Information along a path Information on surface Information inside medium

  25. Talk by F.M.Liu, in Parallel IV, 16:00-(Thur) Direct and Thermal Photon Emission Photons from: Thermal +pQCD L.O. +fragmentation +jet conversion Dynamics is important in estimation of energy loss as well as thermal photon radiation. F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:0807.4771[hep-ph].

  26. Summary • Current status of dynamical modeling in relativistic heavy ion collisions. • Glauber I.C. + QGP fluid + hadron gas • J/psi suppression • Heavy quark diffusion • Direct photon emission • Towards establishment of “Observational QGP physics”

  27. References and Collaborators • Hydro+Cascade: • T.Hirano, U.W.Heinz, D.Khaezeev, R.Lacey, Y.Nara • Phys.Lett.B636, 299 (2006); J.Phys.G34, S879 (2007); • Phys. Rev. C77, 044909 (2008). • Eccentricity fluctuation effects on v2: • T.Hirano, Y.Nara, work in progress. • J/psi suppression: • T.Gunji, H.Hamagaki, T.Hatsuda, T.Hirano, Phys.Rev. • C76, 051901 (2007). • Heavy quark diffusion: • Y.Akamatsu, T.Hatsuda, T.Hirano, arXiv:0809.1499 [hep-ph] • Photon production: • F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:0807.4771 • [hep-ph].

  28. 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)

  29. 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)

  30. 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?

  31. T.Hirano and Y.Nara(’02-) Current Status of Dynamical Modeling in H.I.C. in Our Study CGC Geometric Scaling Before collisions “DGLAP region” Transverse momentum Shattering CGC (N)LOpQCD Parton production Pre- equilibrium Glasma fluctuation Instability? Equilibration? • Parton energy loss • Inelastic • Elastic Interaction • Hydrodynamics • viscosity • non chem. eq. “Perfect” fluid QGP or GP Recombination Coalescence Dissipative hadron gas Hadronic cascade Fragmentation Proper time Low pT Intermediate pT High pT

  32. 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

  33. 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)

  34. 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-))

  35. 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)

  36. 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]

  37. 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

  38. 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

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

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

  41. 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)

  42. 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

  43. QGP shines at pT~3 GeV/c Thermal emission is dominant at low pT. Emission from QGP is dominant at ~3GeV/c

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