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Hydrodynamic Modeling of Heavy Ion Collisions

ATHIC2008 Tsukuba University, Tsukuba, Japan October 13-15, 2008. Hydrodynamic Modeling of Heavy Ion Collisions. Tetsufumi Hirano 平野哲文 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 Modeling of Heavy Ion Collisions

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  1. ATHIC2008 Tsukuba University, Tsukuba, Japan October 13-15, 2008 Hydrodynamic Modeling ofHeavy Ion Collisions Tetsufumi Hirano 平野哲文 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. Inputs to Hydro: Multiplicity 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. T.Hirano et al., Phys.Rev.C77, 044909 (2008). pT Spectra for PID hadrons A hybrid model works well up to pT~1.5GeV/c. Other components (reco/frag) would appear above.

  6. T.Hirano et al., Phys.Lett.B636, 299 (2006) 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

  7. T.Hirano et al., Phys.Lett.B636, 299 (2006); Phys.Rev.C77, 044909 (2008). 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.

  8. Centrality Dependence of Differential v2 PHENIX PHENIX Pions, AuAu 200 GeV

  9. Hybrid Model at Work at sqrt(sNN)=62.4 GeV PHENIX PHENIX Pions, AuAu 62.4 GeV

  10. Differential v2 in Au+Au and Cu+Cu Collisions Au+Au Cu+Cu Same Npart, different eccentricity Au+Au Cu+Cu Talk by M. Shimomura Same eccentricity, different Npart

  11. T.Hirano et al., Phys.Rev.C77, 044909 (2008). 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.

  12. Phi-mesons as a Probe at Hadronization

  13. 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.

  14. T.Hirano et al., Phys.Rev.C77, 044909 (2008). 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. T. Hirano and Y. Nara, work in progress 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! CGC initial conditions? Talk by Y. Nara

  18. 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-))

  19. 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)

  20. T. Hirano and U. Heinz, work in progress 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]

  21. 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, source imaging,…)

  22. 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

  23. 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)

  24. T. Gunji et al. Phys. Rev. C 76:051901 (R), 2007; J.Phys.G: Nucl.Part.Phys. 35, 104137 (2008). Best fit @ (TJ/y, Tc, fFD) = (2.00Tc, 1.34Tc, 10%) 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.) • TJ/ycan be determined in a narrow region. Talk by T. Gunji

  25. 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

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

  27. 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

  28. F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv:0807.4771[hep-ph]. 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. Talk by F.M. Liu

  29. 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”

  30. 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). • Elliptic flow scaling: • M.Shimomura, S.Esumi, T.Hirano, Y.Nara, work in progress. • Eccentricity fluctuation effects on v2: • T.Hirano, Y.Nara, work in progress. • Source function: • T.Hirano and U.Heinz, 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].

  31. 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)

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