#### Transcript Hydrodynamic Approaches to Relativistic Heavy Ion Collisions

Hydrodynamic Approaches to Relativistic Heavy Ion Collisions Tetsufumi Hirano RIKEN BNL Research Center Contents • Introduction: dynamics of heavy ion collisions • Hydrodynamic Models – Equation of State – Initial Condition – Freezeout • Success and Failure of Hydrodynamic approaches at RHIC – Elliptic Flow – HBT puzzle • Summary Introduction 1: Space-Time Evolution of Heavy Ion Collision photons leptons Hadron phase jets t hadrons Cross over? z x QGP phase Reaction plane Time scale ~10 fm/c 0 z (collision axis) Introduction 2: Static to Dynamic STATIC QCD matter Lattice QCD simulations Matter produce in heavy ion collisions is DYNAMIC. •Space-time evolution •Expansion •Cool down •Phase transition •… One possible description is HYDRODYNAMICS. F.Karsch et al. (’00) •Powerful and reliable •1st principle calculations •Currently, small size and no time evolution Full 3D simulation by T.H. and Y.Nara (’04) Basics of Hydrodynamics Hydrodynamic Equations Energy-momentum conservation Charge conservations (baryon, strangeness, etc…) For perfect fluids (neglecting viscosity), Need equation of state (EoS) P(e,nB) Energy density Pressure 4-velocity to close the system of eqs. Hydro can be connected directly with lattice QCD Within ideal hydrodynamics, pressure gradient dP/dx is the driving force of collective flow. Collective flow is believed to reflect information about EoS! Phenomenon which connects 1st principle with experiment Caveat: Thermalization, l << (typical system size) Inputs for Hydrodynamic Simulations Final stage: Free streaming particles Need decoupling prescription t Intermediate stage: Hydrodynamics can be valid if thermalization is achieved. Need EoS z Need modeling (1) EoS, (2) Initial cond., and (3) Decoupling Initial stage: Particle production and pre-thermalization beyond hydrodynamics Instead, initial conditions for hydro simulations Main Ingredient: Equation of State One can test many kinds of EoS in hydrodynamics. Typical EoS in hydro model Latent heat Lattice QCD predicts cross over phase transition. Nevertheless, energy density explosively increases in the vicinity of Tc. Looks like 1st order. F.Karsch et al. (’00) From P.Kolb and U.Heinz(’03) H: resonance gas(RG) Q: QGP+RG Lattice QCD simulations Interface 1: Initial Condition •Need initial conditions (energy density, flow velocity,…) Initial time t0 ~ thermalization time •Take initial distribution from other calculations •Parametrize initial hydrodynamic field T.H.(’02) y y x x ex.) In transverse plane, energy density or entropy density prop. to # of participants, # of binary collisions, or etc. x Energy density from NeXus. (Left) Average over 30 events (Right) Event-by-event basis (Talk by Hama) Interface 2: Freezeout Need translation from thermodynamic variables to particle spectra to be observed. Sudden freezeout (Cooper-Frye formula) Continuous particle emission (Talk by Hama) Hadronic afterburner via Boltzmann eq. QGP Fluid QGP Fluid QGP Fluid Hadronic Hadron Fluid l=0 Escaping probability P Tf.o. l=infinity t ffree(x,p)=Pf(x,p) Cascade (RQMD, UrQMD) Teaney, Lauret, Shuryak Bass, Dumitru … Hydrodynamic Models @ RHIC There are many options: In addition, •Initial conditions Dimension •Parametrization • Boost inv. (Bjorken, ’83) •Taken from other model • 1D(r) + boost inv. •With/without fluctuation + cylindrical sym. •EoS • 2D(x,y) + boost inv. •Lattice inspired model • Full 3D •With/without phase transition • Cartesian (t,x,y,z) •With/without chemical freeze out • t-h coordinate •Decoupling •Sudden freezeout •Continuous emission Each option reflects •Hadronic cascade what one wants to study. Success of Hydrodynamics Ollitrault (’92) --Elliptic Flow-- Talk by Voloshin How the system respond to initial spatial anisotropy? Free streaming Hydrodynamic expansion y f x INPUT Rescattering OUTPUT 0 f 2p Final momentum anisotropy 2v2 dN/df dN/df Initial spatial anisotropy 0 f Boltzmann to Hydro !? Molnar and Huovinen (’04) elastic cross section 47mb ~ inelastic cross section of pp at RHIC energy!? Still ~30% smaller than hydro result! Hydro (l~0) is expected to gain maximum v2 among transport theories. “hydrodynamic (maximum) limit” Hydrodynamic Results of v2/e Kolb, Sollfrank, Heinz (’00) LHC? (response)=(output)/(input) STAR(’02) Number density per unit transverse area • Dimension • 2D+boost inv. • Initial condition • Parametrization • EoS • QGP + RG (chem. eq.) • Decoupling • Sudden freezeout •Hydrodynamic response is const. v2/e ~ 0.2 @ RHIC •Exp. data reach hydrodynamic limit at RHIC for the first time. •Exp. line is expected to bend at higher collision energy. Hydrodynamic Results of v2(pT,m) PHENIX(’03) Huovinen et al.(’01) • Dimension • 2D+boost inv. • Initial condition • Parametrization • EoS • QGP + RG (chem. eq.) • Decoupling • Sudden freezeout • Correct pT dependence up to pT=1-1.5 GeV/c • Mass ordering • Deviation in intermediate ~ high pT regions Other physics • Jet quenching (Talk by Vitev) • Recombination (Talk by Hwa) • Not compatible with particle ratio Need chem. freezeout mechanism Hydrodynamic Results of v2(h) •Hydrodynamics works only at midrapidity? •Forward rapidity at RHIC ~ Midrapidity at SPS? Heinz and Kolb (’04) T.H. and K.Tsuda(’02) • Dimension • Full 3D (t-h coordinate) • Initial condition • Parametrization • EoS 1. QGP + RG (chem. eq.) 2. QGP + RG (chem. frozen) • Decoupling • Sudden freezeout Hydrodynamic Results of v2 (again) Teaney, Lauret, Shuryak(’01) • Dimension • 2D+boost inv. • Initial condition • Parametrization • EoS • Parametrized by latent heat (LH8, LH16, LH-infinity) • RG • QGP+RG (chem. eq.) • Decoupling • Hadronic cascade (RQMD) • Large gap (~50% reduction) at SPS comes from finite l or “viscosity”. • Latent heat ~0.8 GeV/fm3 is favored. • Hadronic afterburner explains forward rapidity? (T.H. and Y.Nara, in progress) Summary for Success of Hydrodynamics • Description of elliptic flow parameter v2 • v2(pT,m) • Up to 1-1.5 GeV/c • v2(h) • Near midrapidity • Multiplicity dependence • Need cascade/viscosity for hadrons • Phase transition with latent heat ~ 0.8 GeV/fm3 is favored Future study: • Forward rapidity by hydro+hadronic cascade • Viscosity in QGP • A lot of work should be done… Failure of Hydrodynamics by Magestro, --HBT puzzle-- Talks Csorgo and Hama Bird’s eye view p1 View from beam axis y Rside KT q Rlong p2 Rout x z C2 2 Two particle corr. fn. 1 1/R q Source Function and Flow Long wave length Short wave length Source fn. Midrapidity & cylindrical symmetry x-y x-t Source fn. from hydro From P.Kolb and U.Heinz(’03) KT: “Wave length” to extract radii Rout/ Rside Rlong Rout Rside Sensitivity to Chemical Composition T.H. and K.Tsuda (’02) • Dimension • Full 3D (t-h coordinate) • Initial condition • Parametrization • EoS 1. QGP + RG (chem. eq.) 2. QGP + RG (chem. frozen) • Decoupling • Sudden freezeout DASHED LINE SOLID LINE •Rout/ Rside(hydro) > Rout/ Rside(data)~1 HBT puzzle!!! •HBT radii reflects last interaction points. Problem of sudden freezeout? Note that exp. data of Rout/Rside slightly increase by considering core-halo picture Sensitivity to Freezeout (contd.) Soff, Bass, Dumitru (’01) • Dimension Hydro+cascade 200 1D+boost inv. + cylindrical sym. Hydro 160 • Initial condition Parametrization • EoS Hydro+cascade 160 QGP + RG (chem. eq.) Hydro 200 • Decoupling Hadronic afterburner by UrQMD STAR PHENIX Taken from D. Magestro, talk @ QM04 HBT radii from continuous particle emission model Talk by Hama •Better in low pT region for Tc=160 MeV case by smearing through cascade. Still something is missing to interpret the data. (Absolute value?) x-t Correlation of Source Function Why hydro doesn’t work? positive! Positive? Negative? Rout~Rside may require positive x-t corr. t Typical source fn. from hydro x Negative x-t correlation t Hubble like flow? Csorgo et al. x Positive x-t correlation Summary and Outlook • From elliptic flow point of view, a hydro + cascade (RQMD) model with latent heat 0.8 GeV/fm3 gives a good description at both SPS and RHIC (in low pT and near midrapidity). Need full 3D hydro + hadronic cascade (a possible model to describe all rapidity region at RHIC) • However, a similar model (hydro + UrQMD) fails to reproduce HBT radii. Need a thorough search for initial conditions Need more sophisticated description of the late stage (HBT is a quantum effects!)