Hydrodynamic Modeling of Heavy Ion Collisions Tetsufumi Hirano 平野哲文 Department of Physics The University of Tokyo The University of Tokyo ATHIC2008 Tsukuba.

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Hydrodynamic Modeling of Heavy Ion Collisions Tetsufumi Hirano 平野哲文 Department of Physics The University of Tokyo The University of Tokyo ATHIC2008 Tsukuba University, Tsukuba, Japan October 13-15, 2008 ATHIC2008 Tsukuba University, Tsukuba, Japan October 13-15, 2008 “Hydrodynamics and Flow”, T. Hirano, N. van der Kolk, A. Bilandzic, arXiv:

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

QGP fluid + hadronic cascade in full 3D space 0 collision axis time Au QGP fluid Initial condition (=0.6fm): 1.Glauber model 2.(CGC model) QGP fluid: 3D ideal hydrodynamics (T c = 170 MeV) Massless free u,d,s+g gas + bag const. Hadron phase: 1.T th =100MeV 2.Hadronic cascade (JAM) (T sw = 169 MeV) hadron gas Hybrid approaches: (1D) Bass, Dumitru (2D) Teaney, Lauret, Shuryak (3D) Nonaka, Bass, Hirano et al.

Inputs to Hydro: Multiplicity 1.Glauber model N part :N coll = 85%:15% 2. CGC model Matching I.C. via e(x,y, s ) Centrality dependenceRapidity dependence Kharzeev, Levin, and Nardi Implemented in hydro by TH and Nara

p T Spectra for PID hadrons A hybrid model works well up to p T ~1.5GeV/c. Other components (reco/frag) would appear above. T.Hirano et al., Phys.Rev.C77, (2008).

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

Differential v 2 & Centrality Dependence Mass dependence is o.k. Note: First result was obtained by Teaney et al % Centrality dependence is ok Large reduction from pure hydro in small multiplicity events T.Hirano et al., Phys.Lett.B636, 299 (2006); Phys.Rev.C77, (2008).

Centrality Dependence of Differential v 2 Pions, AuAu 200 GeV PHENIX

Hybrid Model at Work at sqrt(s NN )=62.4 GeV Pions, AuAu 62.4 GeV PHENIX

Differential v 2 in Au+Au and Cu+Cu Collisions Same N part, different eccentricity Au+Au Cu+Cu Same eccentricity, different N part Au+Au Cu+Cu Talk by M. Shimomura

Mass Ordering for v 2 (p T ) Mass dependence is o.k. from hydro+cascade % Proton Pion Mass ordering comes from hadronic rescattering effect. Interplay btw. radial and elliptic flows. T.Hirano et al., Phys.Rev.C77, (2008).

Phi-mesons as a Probe at Hadronization

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

Violation of Mass Ordering for  -mesons in p T < 1 GeV/c Just after hadronizationFinal results T = T sw = 169 MeV b=7.2fm Caveat: Published PHENIX data obtained in p T >~1GeV/c for  mesons Violation of mass ordering for phi mesons! Clear signal of early decoupling! T.Hirano et al., Phys.Rev.C77, (2008).

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

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 over events E.g.) b min = 0.0fm b max = 3.3fm in Au+Au collisions at 0-5% centrality

Effect of Eccentricity Fluctuation on v 2 v 2 (w.rot) ~ 2 v 2 (w.o.rot) at N part ~350 in AuAu v 2 (w.rot) ~ 4 v 2 (w.o.rot) at N part ~110 in CuCu CGC initial conditions? Significant effects of fluctuation! Talk by Y. Nara T. Hirano and Y. Nara, work in progress

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

Distribution of the Last Interaction Point from Hydro + Cascade Blink: Ideal Hydro, no resonance decays Kolb and Heinz (2003) x-t x-y p x ~ 0.5 GeV/c for pions Long tail (  decay? elastic scattering?) Positive x-t correlation

1D (Angle-averaged) Source Function from Hydro + Cascade 0.48 < K T <0.6 GeV/c0.2 < K T <0.36 GeV/c Broader than PHENIX data Almost no K T dependence  ?  PHENIX data Significant effects of hadronic rescatterings K T =P T /2 PHENIX, PRL98,132301(2007); arXiv: [nucl-ex] T. Hirano and U. Heinz, work in progress

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, … )

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

J/psi Suppression M.Asakawa and T.Hatsuda, PRL. 92, (2004) A. Jakovac et al. PRD 75, (2007) G.Aarts et al. arXiv: [hep-lat]. (Full QCD) See also T.Umeda,PRD75,094502(2007) Quarkonium suppression in QGP Color Debye Screening T.Matsui & H. Satz PLB (1986) Suppression depends on temperature (density) and radius of QQbar system. T J/psi : 1.6T c ~2.0T c T , T  ’ : ~ 1.1T c May serve as the thermometer in the QGP.

Results from Hydro+J/psi Model Best (T J/, T , f FD ) = (2.00T c, 1.34T c, 10%) Bar: uncorrelated sys. Bracket: correlated sys. Onset of J/ suppression at N part ~ 160. (  Highest T at N part ~160 reaches to 2.0T c.) T J/ can be determined in a narrow region. Contour map 1122 T. Gunji et al. Phys. Rev. C 76: (R), 2007; J.Phys.G: Nucl.Part.Phys. 35, (2008). Talk by T. Gunji

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

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

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

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: [hep-ph]. Talk by F.M. Liu

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 ”

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, (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, (2007). Heavy quark diffusion: Y.Akamatsu, T.Hatsuda, T.Hirano, arXiv: [hep-ph] Photon production: F.-M.Liu, T.Hirano, K.Werner, Y.Zhu, arXiv: [hep-ph].

Why they shift oppositely? protonspions pTpT v 2 (p T ) v2v2 must decrease with proper time v 2 for protons can be negative even in positive elliptic flow TH and M.Gyulassy, NPA769,71(06) P.Huovinen et al.,PLB503,58(01)