Hydrodynamic Approach: Open Issues

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”. • Hadron Spectra • Fragmentation • ReCo • Cascade (hydro) pQCD jet sQGP HYDRO lQCD cQCD thermalization lepton, photon

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

4. Open Issues • Open Issues in hydro + cascade models • Hybrid approach helps to understand v2(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 v2 • Low density • Deviation from hydro • Forward rapidity at RHIC • ~ Midrapidity at SPS? • Heinz and Kolb (’04) T.H. and K.Tsuda(’02) • Dimension • Full 3D(t-hs coordinate) • EoS • QGP + hadrons (chem. eq.) • QGP + hadrons (chem. frozen) • Decoupling • Sudden freezeout

8. T.H., talk at RHIC II Science Workshop (probe of EOS session) Apr.29 Proposal No.2 • Need a new hydro + cascade model in full 3D (t, h, x, y)coordinate • Full 3D hydro in t-h 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.

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) In coming particle flux Out going particle flux ds Flow S 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?

11. Cheng et al(2002) 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? r: Interaction range

12. Example Oversampling factor l: N  lN Cross section s: s  s/l l infinity  Local

13. Open Issues • Open Issues in hydro + cascade models • Hybrid approach helps to understand v2(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! Hydro information Blast Wave Recombination Jet quenching CGC etc. feedback?

15. Az Blast Wave by Lisa & Retiere ReCo(Duke) 200GeV Vr vs. Tth (175,0.55) Single F.O. by Broniowski & Florkowski 130GeV T.H. and K.Tsuda (’02) Hydro: Au+Au at sqrt(sNN) = 130 GeV tau0 = 0.6fm/c Tc Blast Wave by Burward-Hoy 130GeV

16. <Vr> @ 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 t0=0.6fm/c. No pre-thermal diffusion. The sQGP gives just <vr>=0.2-0.3!

17. ReCo Really Suggests Deconfinement Signal? Multi-strangeness sector may directly probe partonic collective flow. However, (T,vT)=(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 R.Fries et al.(2003)

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

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

20. How to Get Large Radiiwithout Spoiling Single Spectra? T.H. and K.Tsuda(’02) Blast Wave Model (M.Lisa & F.Retiere) Partial Chemical Eq. Tth and b are consistent with hydro. But… Rin ~11 fm Rout~12 fm J.Cramer & G.Miller R~13fm Hadronic afterburner helps?

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

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

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 wonderwhether in the mean time you have considered  theeffect of resonances on HBT (in your papernucl-th/0205043 you explicitly mention this fact). Ourexperience at SPS, cf. e.g. Weiner, Phys. Reports 327(2000) 249-346, in particular page 319 tells me thatconsideration of resonances might solve the HBT "puzzle". Most recently Akkelin, Syniukov nucl-th/0310036 havereached the same conclusion.

27. HBT from AMPT • Source is non-Gaussian. • Positive x-t correlation • Not only w decay, but also “thermal” p Hydro (Kolb&Heinz) Xside 30 Lin, Ko, Pal(2002) tau (fm/c) Xout Completely different source shape/size

28. Parton Density from Two Different Models T.H. and Y.Nara (’04) I.Vitev, nucl-th/0404052 Input: dNch/dh Output: Input: RAA Output: consistent?

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

30. 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. Jet Tomography  Chemical Composition of sQGP

31. Unified DescriptionBased 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. T.H. and Y.Nara (’02-) Toward a Unified Model (near future?) Nuclear wave function Parton distribution CGC (a la KLN) Color Quantum Fluid(QS2<kT2<QS4/L2) (x-evolution eq.) Collinear factorized Parton distribution (CTEQ) (MV model 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 Hadron gas Hadronic cascade (JAM) Recombination Freezeout (chemical & thermal) Fragmentation Proper time Low pT Intermediate pT High pT

33. How does one connect CGC with sQGP? Thermalization/Isotropization? Initial condition of hydrodynamic simulations Gluons produced from two CGC collisions (KLN) 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 (KNV)  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.

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

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

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

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

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 (>Tc) • transverse flow •  Safe to use hydro data T>Tc @ (t, x, y, hs) • Applying suggestion: • Parton Energy Loss • Recombination • Thermal photon • All depend on your idea!!! HYDRO MODEL

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 1st order • getglv1sts(tau,x,y,eta,p0): • GLV 1st order neglecting kinematics • moliere(p0): Elastic scattering angle • opacityela(p0,opa): Elastic scattering angle at chi

44. Example