1. Elliptic Flow from Hydro (short review) 2. Hydrodynamic afterburner for the CGC at RHIC

1. 1. Elliptic Flow from Hydro(short review)2. Hydrodynamic afterburner for the CGC at RHIC Tetsufumi Hirano RIKEN BNL Research Center Hot Quarks 2004 Taos Valley, NM

2. Outline (part 1) Apology: It’s hard to discuss all topics within 15-20 min… • I just pick up some results from hydro Elliptic flow Basics of hydrodynamics Results from hydrodynamic simulations Summary

3. Free streaming dN/df 0 f 2p Elliptic Flow Ollitrault (’92) How does the system respond to initial spatial anisotropy? Hydrodynamic expansion y f x INPUT Initial spatial anisotropy 2v2 Rescattering dN/df OUTPUT Final momentum anisotropy 0 f 2p

4. Boltzmann to Hydro !? Molnar and Huovinen (’04) 47mb ~ inelastic cross section of pp at RHIC energy!? Still ~30% smaller than hydro result! elastic cross section Hydro (l~0) is expected to gain maximum v2 among transport theories.  “hydrodynamic (maximum) limit”

5. 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) to close the system of eqs.  Hydro can be connected directly with lattice QCD Energy density Pressure 4-velocity 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

6. Inputs for Hydrodynamic Simulations Final stage: Free streaming particles  Need decoupling prescription t Intermediate stage: Hydrodynamics can be applied if thermalization is achieved.  Need EoS z Initial stage: Particle production and pre-thermalization beyond hydrodynamics • Instead, initial conditions for hydro simulations

7. Main Ingredient: Equation of State One can test many kinds of EoS in hydrodynamics. Typical EoS in hydro model EoS with chemical freezeout H: resonance gas(RG) Q: QGP+RG p=e/3 Kolb and Heinz (’03) T.H. and K.Tsuda(’02) Latent heat PCE:partial chemical equiliblium CFO:chemical freeze out CE: chemical equilibrium

8. 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 y y T.H.(’02) x x x Energy density from NeXus. (Left) Average over 30 events (Right) Event-by-event basis e or s proportional to rpart, rcoll or arpart + brcoll

9. Interface 2: Freezeout Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Hirano & Tsuda; Teaney; Kolb & Rapp Teaney, Lauret & Shuryak; Bass & Dumitru Ideal hydrodynamics QGP phase Tc Chemical Equilibrium EOS Partial Chemical Equilibrium EOS Tch Hadronic Cascade Hadron phase Cf.) Continuous particle emission by SPheRIO group Tth Tth t Sudden freezeout: l=0infinity

10. Hydrodynamic Results of v2 Kolb, Sollfrank, Heinz (’00) STAR(’02) • Dimension • 2D+boost inv. • Initial condition • Parametrization • EoS • QGP + RG (chem. eq.) • Decoupling • Sudden freezeout LHC? (response)=(output)/(input) • 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 energies. Number density per unit transverse area

11. Hydrodynamic Results of v2(pT,m) PHENIX(’03) • Correct pT dependence up to pT=1-1.5 GeV/c • Mass ordering • Deviation in intermediate ~ high pTregions  Other physics • Jet quenching (Talk by Vitev) • Recombination (Talk by Fries) • Viscosity • Not compatible with particle ratio • Need chem. freezeout mechanism Huovinen et al.(’01) • Dimension • 2D+boost inv. • Initial condition • Parametrization • EoS • QGP + RG (chem. eq.) • Decoupling • Sudden freezeout

12. Hydrodynamic Results of v2(h) • Hydrodynamics works only at midrapidity? • Forward rapidity at RHIC ~ Midrapidity at SPS? Heinz and Kolb (’04) Heinz,T.H. and Nara (in progress) T.H. and K.Tsuda(’02) • Dimension • Full 3D (t-h coordinate) • Initial condition • Parametrization • EoS • QGP + RG (chem. eq.) • QGP + RG (chem. frozen) • Decoupling • Sudden freezeout

13. 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)

14. Summary of Results

15. Summary for Part 1 Hydrodynamics works well at RHIC? • Perhaps promising • Caveat 1: Hadron phase should be described by viscous fluid/hadronic cascade. Realistic treatments of boundary is also mandatory. • Caveat 2: Don’t forget HBT puzzle! Hydro+cascade? • Need further systematic studies, e.g., hydro+cascade in forward rapidity region, more realistic EoS, unified treatment, viscosity, etc.

16. Hydrodynamic afterburner for the CGC at RHIC In collaboration with Y.Nara Outline (part 2) • Three key topics at RHIC • Hydrodynamics • Jet quenching • Color Glass Condensate (CGC) • CGC+hydro+jet model (CHJ model) • Toward a unified dynamical description for relativistic heavy ion collisions

17. CGC, hydrodynamics, and jet quenching Nuclear modification factor RAA Centrality dependence of dN/dh/(Npart/2) v2(pT) Kharzeev, Levin, Nardi (KLN) … Vitev, Gyulassy, Levai, Wang, Wang, … Kolb, Heinz, Huovinen T.H., Teaney, Shuryak,… These three physics related with each other?

18. Dense Matter at RHIC CGC Gluon multiplicity (QS: saturation scale) Hydrodynamics Mean free path is assumed to be very small: Jet quenching Opacity is large:

19. CGC+Hydro+Jet (CHJ) model Nuclear wave function Parton distribution CGC (a la KLN) Collinear factorized Parton distribution (CTEQ) Transverse momentum Shattering CGC (kT factorization) LOpQCD (PYTHIA) Parton production I do not discuss high pT physics today. Hydrodynamics (full 3D hydro) Parton energy loss (a la Gyulassy-Levai-Vitev) Jet quenching QGP Hadron gas Freezeout (chemical & thermal) Fragmentation Proper time Low pT Intermediate pT High pT

20. dN/dh from a Saturation Model Kharzeev and Levin (’01) ggg Parton-hadron duality f ~1/as Qs2 0 kT2 CGC works well for rapidity and centrality dependences! Clearly, one needs final state interaction!

21. Initial Condition from CGC Saturation scale at a transverse position: where Unintegrated gluon distribution can be written Momentum rapidity y space time rapidityhs Input for hydrodynamic simulations Three parameters: K, l, k  More realistic wave function can be used.

22. Example of a Simulation Space-time evolution of energy density in sqrt(sNN)=200 GeV Au+Au collision at b=7.2fm

23. Results from CHJ model Pseudorapidity dist. pT spectrum Quenched jet Hydro Mean pT Centrality and rapidity dependences are well described by CH(J) model.  What is the role of hydro in comparison with KLN approach?

24. How ET/N (energy/entropy) evolves in CHJ model? Initial condition of hydrodynamic simulations Gluons produced from two CGC collisions Final (psuedo)rapidity spectra of all hadrons ET/N ~ 1.6 GeV ET/N ~ 1.0 GeV ET/N ~ 0.55 GeV  Consistent with classical Yang Mills on 2D lattice  Consistent with exp. data ~0.6 GeV This should be obtained through non-equilibrium processes.  Production of entropy Hydrodynamic evolution “PdV work” reduces ET/N.

25. Toward a Unified Model Nuclear wave function Parton distribution CGC (a la KLN) Color Quantum Fluid(QS2<kT2<QS4/L2) (x-evolution eq.) Collinear factorized Parton distribution (CTEQ) (classical Yang-Mills on 2D lattice) Transverse momentum Parton production (dissipative process?) Shattering CGC (kT factorization) LOpQCD (PYTHIA) (classical Yang-Mills on 2D lattice) important in forward region Hydrodynamics (full 3D hydro) Parton energy loss (a la Gyulassy-Levai-Vitev) Jet quenching QGP Recombination (via string fragmentation) Hadron gas Hadronic cascade (JAM) Freezeout (chemical & thermal) Fragmentation Proper time Low pT Intermediate pT High pT

26. Summary and Outlook for Part 2 • First step toward a unified and dynamical approach to relativistic heavy ion collisions (CHJ model) • Each component can be improved. • CGC: Realistic wave function, classical YM on lattice, … • Hydro: Realistic EoS from lattice QCD, rate eq. for QGP, … • Jet: Species dependent energy loss, fluctuations, … • Another idea can be plugged in this approach. • Hadronic cascade • Recombination • Etc. A big problem on thermalization remains!

27. SPARE SLIDES

28. Elliptic Flow Generatedin Early Stage Kolb and Heinz (’03) “Elliptic flow” is believed to be sensitive to the early dynamics. Wait! Is the momentum anisotropy epobservable ?

29. RG+QGP “hard” EoS Ultrarelativistic pion gas Pressure Resonance Gas (RG) “soft” EoS Rescale e (GeV/fm3) 0 20 EoS dependence of v2(pT)  Pion elliptic flow is insensitive to EoS.  What makes a difference of proton elliptic flow?

30. Anisotropic Flow y f x z x Transverse plane Reaction plane A.Poskanzer & S.Voloshin (’98) “Flow” is not a good terminology especially in high pT regions due to jet quenching. 0th: azimuthally averaged dist.  radial flow 1st harmonics: directed flow 2nd harmonics: elliptic flow …

31. Large radial flow reduces v2 for protons High pT protons Radial flow pushes protons to high pT regions Low pT protons are likely to come from fluid elements with small radial flow Low pT protons Even for positive elliptic flow of matter, v2 for heavy particles can be negative in low pT regions!

32. v2(pT,m) from hydro(+cascade) Results from (1) partial chemical equilibrium EoS Results from (1) chemical equilibrium EoS or (2) resonance gas EoS (no QGP) or (3) hydro+RQMD pion v2/e proton v2/e Compiled by C.Ogilvie

33. pT distribution from PCE • Up to what pT do we need to reproduce data by hydro? • Recombination? • Baryon junction? • What is initial collective flow? • Classical YM on lattice may help… P.Kolb and R.Rapp(’03) Dashed line: Initial transverse kick Solid line: a=0

34. v2(pT) Stalls in Hadron Phase? Hadronic rescattering via RQMD does not change v2(pT) for p ! Mechanism for stalling v2(pT) • Hydro (chem. eq.): Pion dominance Effect of EoS • Hydro+RQMD: Effective viscosity Effect of finite l D.Teaney(’02) Pb+Pb, SPS 17 GeV, b=6 fm Solid lines are guide to eyes

35. How ep is distributed to hadrons? Partial Chemical Equilibrium Chemical Equilibrium p Tth PCE leads to overestimation of v2(pT) for p when radial flow is large enough to reproduce pT distribution. radial flow K T.H. and K.Tsuda (’02) Proton v2(pT) p Pions v2(pT) pions pions CE PCE ep ep kaons kaons protons protons

36. Comparison of CE with PCE EOS Time Evolution

37. Comparison CE with PCE (contd.) Tth dependence

38. Hadronic Cascade Will Help? T.H.(’01) STAR (’02) Forward rapidity at RHIC ~ Midrapidity at SPS? “Thermalization coeff.”? Hydro: P.Kolb et al.(’00)

39. Sensitivity to Freezeout (contd.) Soff, Bass, Dumitru (’01) • Dimension 1D+boost inv. + cylindrical sym. • Initial condition Parametrization • EoS QGP + RG (chem. eq.) • Decoupling Hadronic afterburner by UrQMD Hydro+cascade 200 Hydro 160 Hydro+cascade 160 Hydro 200 STAR PHENIX • It is getting better in low pT region for Tc=160 MeV case by smearing through cascade. • Still something is missing to interpret the data. Taken from D. Magestro, talk @ QM04 HBT radii from continuous particle emission model?

40. Hydro + Rate Eq. in QGP phase T.S.Biro et al.,Phys.Rev.C48(’93)1275. Including ggqqbar and ggggg Collision term: Assuming “multiplicative” fugacity, EoS is unchanged.