1. Hydrodynamic Approach: Open Issues Tetsufumi Hirano Special thanks to Nu Xu, Miklos Gyulassy and Denes Molnar The Berkeley School, LBNL, CA, May 27, 2005

2. Before Discussion Hydrodynamics is the heart of dynamical model in H.I.C. Some of the open questions are highly related with “Two particle correlation” and “thermal model”. sQGP HYDRO lQCD cQCD thermalization Hadron Spectra Fragmentation ReCo Cascade (hydro) jet pQCD lepton, photon

3. 5. Summary Open our mind ! Hydrodynamics can be used even for “high p T physics in HIC”. Open our mind ! Hydrodynamics can be used even for “high p T physics in HIC”. – Jet tomography – EM probe – (J/  suppression) – … Keep in mind ! Keep in mind ! How robust is the current agreement of hydro?: How robust is the current agreement of hydro?: – Chemical non-eq.? – Initial fluctuation? – Viscosity? – Thermalization? – EoS? – (Freeze-out?) Hydrodynamics is one of the valuable tools at RHIC energies T.H., “Hydrodynamic Models”, talk at QM2004

4. Open Issues Open Issues in hydro + cascade models –Hybrid approach helps to understand v 2 (eta)? –Boundary? Transport Properties? How well the hydrodynamics works? Check the consistency (ReCo, B.W., etc.) Feedback from other approaches? (Large source radius, chemical composition, etc.) Still need to check resonance effects on HBT? A “unified” dynamical approach based on hydro? (How large viscous effects?) How can one profit from hydro? Open source? “Hydro-Lite” model (Easy way to check consistensy)

5. Full 3D hydro + cascade

6. Lessons from My Talk on May 19 Dissipative hadronic corona of the “perfect fluid” sQGP core is important. Ideal hydro description for hadronic matter is ruled out! (You should refer to Teaney’s results from now!) One should pay attention to accidental reproduction of data a little bit more! Bold assumptions sometimes cause a big mistake! As many data as possible within one dynamical approach.

7. Rapidity Dependence of v 2 Dimension Full 3D (  s coordinate) EoS 1.QGP + hadrons (chem. eq.) 2.QGP + hadrons (chem. frozen) Decoupling Sudden freezeout Low density  Deviation from hydro Forward rapidity at RHIC ~ Midrapidity at SPS? Heinz and Kolb (’04) T.H. and K.Tsuda(’02)

8. Proposal No.2 Need a new hydro + cascade model in full 3D (  x, y) coordinate –Full 3D hydro in  -  coordinate T.H. or SPheRIO group (Brazil) –Combine hydro with one of the hadronic cascade models (Self proposal?!) –Extension of current hydro + cascade Bass & Dumitru, (1+1)D hydro + UrQMD Teaney, Lauret & Shuryak, (2+1)D hydro + RQMD We desperately need people to do the above study. T.H., talk at RHIC II Science Workshop (probe of EOS session) Apr.29

9. Caveats for a Hybrid Approach Caveat1: Boundary btw. hydro and cascade (comment by Bugaev) Caveat2: How reliable viscosity is in hadronic cascade? (comments by Molnar, (Pratt), Gyulassy) Both Problems need quantitative discussion

10. Boundary btw. hydro and cascade Cooper-Frye formula (1972)  Out going particle flux In coming particle flux To obey the energy momentum conservation, in-coming flux is mandatory. Obviously, it depends on flow profile. How large at RHIC? How does dynamics change? Flow dd

11. Open Issues in Hadronic Cascade (with a help by D.Molnar) r This instant interaction leads to acausal propagation especially in high particle density. How (un)realistic the viscous effects from hadronic cascade? The scheme might introduce unwanted viscous effect. Does hydro+cascade make full use of “artificial” viscosity to get excellent agreement with data? Cheng et al(2002) r: Interaction range

12. Example Oversampling factor : N  N Cross section  :     infinity  Local

13. Open Issues Open Issues in hydro + cascade models –Hybrid approach helps to understand v 2 (eta)? –Boundary? Transport Properties? How well the hydrodynamics works? Check the consistency (ReCo, B.W., etc.) Feedback from other approaches? (Large source radius, chemical composition, etc.) Still need to check resonance effects on HBT? A “unified” dynamical approach based on hydro? (How large viscous effects?) How can one profit from hydro? Open source? “Hydro-Lite” model (Easy way to check consistensy)

14. Consistency Check! Blast Wave Recombination Jet quenching CGC etc. feedback? information

15. V r vs. T th T.H. and K.Tsuda (’02) Hydro: Au+Au at sqrt(s NN ) = 130 GeV tau 0 = 0.6fm/c ReCo(Duke) 200GeV TcTc Single F.O. by Broniowski & Florkowski 130GeV Blast Wave by Burward-Hoy 130GeV Az Blast Wave by Lisa & Retiere (175,0.55)

16. @ Hadronization @ Hadronization Model: CGC+Hydro(+Jet), T.H. and Y.Nara (2004) Impact parameter: b=2.4 fm (0-6% centrality) Initial parameters tuned to reproduce PHOBOS dN/deta with  0 =0.6fm/c. No pre-thermal diffusion.  0 (fm/c) | |  |<0.5 0.10.30 1.00.27 3.00.18 The sQGP gives just =0.2-0.3!

17. ReCo Really Suggests Deconfinement Signal? R.Fries et al.(2003) Multi-strangeness sector may directly probe partonic collective flow. However, (T,v T )=(175,0.55) is gigantic! Accidental? Do we need another mechanism? UrQMD gives mass ordering and approximate scaling elliptic flow. (Hydro+jet model also does.) Blast wave  next slide

18. Blast Wave Fit for  ? Hydro (PCE) central What is important is interpretation after fitting.

19. Approximate Hydro Line T.H. and M.Gyulassy B.W.model

20. How to Get Large Radii without Spoiling Single Spectra? Blast Wave Model (M.Lisa & F.Retiere) R in ~11 fm R out ~12 fm J.Cramer & G.Miller R~13fm T.H. and K.Tsuda(’02) Partial Chemical Eq. Hadronic afterburner helps? T th and  are consistent with hydro. But…

21. Initial Transverse Flow Hubble constant H = 0.25/fm Chojnacki et al.(2005)

22. Initial Transverse Flow and Spectra H = 0.02/fm << 0.25/fm P.Kolb and R.Rapp(2002) What is the origin? Isotherm f.o.? F.O. prescription?

23. Although I already told hydro+cascade approach is important… A revisit HBT radii from hydro How large the effect of resonance decays on HBT radii in hydro? Nobody checks at RHIC energies. Is it worth checking it? KK correlation? I don’t believe this directly solves the puzzle. However, it would be nice to check it!

24. Source fn.? Hydro? Tomasik & Wiedemann, hep-ph/0210250, page 31 Source function: Resonance effects negligible Hydro: Increase HBT radii (Schlei et al.(1996)) ???????

25. HBT puzzle

26. Results from Hydro at SPS Richard M. Weiner wrote: Dear Tetsufumi Hirano, I read with interest some of your papers and wonder whether in the mean time you have considered the effect of resonances on HBT (in your paper nucl-th/0205043 you explicitly mention this fact). Our experience at SPS, cf. e.g. Weiner, Phys. Reports 327 (2000) 249-346, in particular page 319 tells me that consideration of resonances might solve the HBT "puzzle". Most recently Akkelin, Syniukov nucl-th/0310036 have reached the same conclusion.

27. HBT from AMPT Lin, Ko, Pal(2002) Source is non- Gaussian. Positive x-t correlation  Not only  decay, but also “thermal”  X out X side Hydro (Kolb&Heinz) 30 tau (fm/c) Completely different source shape/size

28. Parton Density from Two Different Models I.Vitev, nucl-th/0404052 Input: R AA Output: T.H. and Y.Nara (’04) Input: dN ch /d  Output: consistent?

29. Chemical Composition of QGP? Jet tomography: “Color charge density” Hydrodynamics: Parton density cf.) Parton density in chem. eq. Not complete chem. eq.!  Need chemical non-eq. description rate eq. for n g and n q (N f =3), (N f =2) > <

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

31. Unified Description Based on Hydro Is this the right approach in H.I.C. (I strongly believe the answer is YES.) If so, what is the first priority problem to be solved near future? What is the outstanding problem? What is missing?

32. Toward a Unified Model (near future?) Proper time Transverse momentum CGC (a la KLN) Color Quantum Fluid (Q S 2 <k T 2 <Q S 4 /  2 ) (x-evolution eq.) Shattering CGC (k T factorization) Hydrodynamics (full 3D hydro) Parton energy loss (a la Gyulassy-Levai-Vitev) Hadroniccascade(JAM) Low p T High p T Recombination Collinear factorized Parton distribution (CTEQ) LOpQCD(PYTHIA) Nuclear wave function Parton distribution Parton production (dissipative process?) QGP Hadron gas Fragmentation Freezeout (chemical & thermal) (MV model on 2D lattice) (classical Yang-Mills on 2D lattice) Jet quenching Intermediate p T important in forward region? T.H. and Y.Nara (’02-)

33. Thermalization/Isotropization? How does one connect CGC with sQGP? Gluons produced from two CGC collisions (KLN) E T /N ~ 1.6 GeV Initial condition of hydrodynamic simulations E T /N ~ 1.0 GeVE T /N ~ 0.55 GeV  Consistent with classical Yang Mills on 2D lattice (KNV)  Consistent with exp. data ~0.6 GeV Final (psuedo)rapidity spectra of all hadrons This should be obtained through non-equilibrium processes.  Production of entropy Hydrodynamic evolution  “PdV work” reduces E T /N.

34. How “Perfect” is the sQGP? Reynolds number = (kinetic term)/(viscous term) Dynamics of viscous fluids need to be solved T.H. and M.Gyulassy

35. Dynamics of Viscous Fluids Relativistic Navier-Stokes is notorious equation in the sense that it violates causality. Introducing relaxation terms by hand (Teaney) Solving equations beyond Navier-Stokes (Muronga & Rischke, Chaudhuri & Heinz)

36. Break Down of Naive Navier-Stokes Eq. and a Relaxation Method Non-relativistic case (Based on discussion by Cattaneo (1948))   0: Fourier’s law  : “relaxation time” Parabolic equation (heat equation) ACAUSAL!! Finite  Hyperbolic equation (telegraph equation) Balance eq.: Constitutive eq.: T.H., “Hydrodynamic Models”, talk at QM2004

37. Beyond Navier Stokes: “Extended Thermodynamics” How obtain additional equations? In order to ensure the second law of thermodynamics, one can choose Balance eqs. Constitutive eqs. Muronga, Rischke, Chaudhuri, Heinz

38. Open Source of Hydro? Practical, but important issue in this field

39. Open Source? AZHYDRO Ver.0.0 (2+1) D hydro Author: P.Kolb BJ_HYDRO Ver.1.1 (1+1)D hydro Author:A.Dumitru, D.H.Rischke Do you still want to use simple hydro model in spite of “NO-GO theorem”? Nevertheless, you want to try? If so, I will make our 3D hydro open to public.

40. Everybody thinks like this: Full 3D hydro with jet + CGC? It must be tough! 3D hydro+jet CGC+3D hydro T.H. and Y.Nara (’02-)

41. http://quark.phy.bnl.gov/~hirano /hydrodata/par_evo.html

42. “Hydro Lite” model (unofficial name) --What you can utilize-- Solution of hydrodynamic simulations: Parton density Temperature (>T c ) transverse flow  Safe to use hydro data T>T c @ ( , x, y,  s ) Applying suggestion: Parton Energy Loss Recombination Thermal photon All depend on your idea!!!

43. Functions Current version: getrho(tau,x,y,eta): Local parton density gettemp(tau,x,y,eta): Local temperature getvx(tau,x,y,eta): Local vx getvy(tau,x,y,eta): Local vy Next version: getInitialPosition(b,tau0,x,y,eta0): Initial parton position with binary collision getInitialPosition(p0,phi0): Initial parton momentum with power law tail getglv1st(tau,x,y,eta,p0): GLV 1 st order getglv1sts(tau,x,y,eta,p0): GLV 1 st order neglecting kinematics moliere(p0): Elastic scattering angle opacityela(p0,opa): Elastic scattering angle at chi

44. Example