1. HBT puzzle: from an ideal hydrodynamic point of view Tetsufumi Hirano RHIC/AGS user’s meeting, BNL, NY, June 21, 2005

2. Outline The sQGP core and the dissipative hadronic corona picture T.H. and M.Gyulassy, nucl-th/0506049 How good/bad is the agreement of ideal hydro results with HBT data? Summary

4. Not Only the sQGP But Also … nucl-th/0506049

5. Differential Elliptic Flow is the Key PHENIX white paper, nucl-ex/0410003 elliptic flow p T spectra p 

6. TcTc QGP phase Hadron phase  P artial C hemical E quilibrium EOS CLASS 2 Hirano & Tsuda; Teaney; Kolb & Rapp CLASS 3 Teaney, Lauret & Shuryak; Bass & Dumitru T ch T th H adronic C ascade C hemical E quilibrium EOS T th CLASS 1 Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Ideal hydrodynamics T ~1 fm/c ~3 fm/c ~10-15 fm/c “No-Go theorem” for class 1  see our paper! Modeling of Hadron Phase and Freezeout

7. Cancel between v 2 and in chemical eq. hadron phase pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 pTpT v 2 (p T ) v2v2 T th  Chemical Eq. Chemical F.O. Increase of with  is unrealistic from particle ratio point of view!

8. 1. Ideal hydrodynamics reproduce v 2 (p T ) remarkably well, but not HBT radii. TRUE FALSE 2. v 2 (p T ) is not sensitive to the late hadronic stage. TRUE FALSE TRUE: Ideal Hydrodynamics reproduces neither v 2 (p T ) nor HBT radii at RHIC. TRUE: v 2 (p T ) depends on thermal equilibrium, chemical equilibrium, and viscous effects in the hadron phase. Check Sheet for Prevailing Opinion X X

9. Nearly Perfect Fluid of sQGP Core and the Dissipative Hadronic Corona T.H. and M.Gyulassy (’05) ! Absolute value of viscosityIts ratio to entropy density Nearly perfect fluidity of the sQGP AND imperfect fluidity of hadrons are manifestation of deconfinement!? What makes this sudden behavior?

10. How good/bad is the agreement of ideal hydro results with HBT data?

11. R side, R out, R long from Ideal Hydro SIDEOUT LONG CE: Chemical Eq. PCE: Partial Chem.Eq. No resonance decays

12. Model PCE Model CE Contour(T=const.) T(  ) at origin T.H. and K.Tsuda(’02) (T th )  Lörstad and Sinyukov(1991) proper time  (fm/c) radius x (fm)

13. AzHBT Radii SIDE LONG OUT OUT-SIDE STAR, PRC71, 044906(2005).

14. N part 1/3 scaling? LINE: AuAu200GeV PLOT: AuAu62.4GeV LINE: AuAu200GeV PLOT: CuCu200GeV For dN/d  and v 2 in CuCu collisions, see, T.Hirano et al.,nucl-th/0506058

15. Dilemma between R side and R long SIDE LONG R side (K T =0) ~ 6fm (data) ~ 4fm (hydro) Source size may grow by resonances (  mesons?). Resonance decays also enhance R long !

16. Resonances Enhance HBT Radii          STAR Hydro(sQGP) +RQMD(hadron) (D.Teaney) Steal from S.Pratt’s talk at RIKEN BNL workshop(’03) See also, Soff, Bass, Dumitru Hydro+UrQMD

17. How to Get Large Radii without Spoiling Single Spectra? Blast Wave Model (M.Lisa & F.Retiere) R in-plane ~11 fm R out-of-plane ~12 fm J.Cramer & G.Miller R~12fm T.H. and K.Tsuda(’02) Partial Chemical Eq. Hydro cannot get such a gigantic source radius! T th and  are consistent with hydro. But… radius (fm) proper time  (fm/c)

18. 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) Note: F.O. parameter  A set of T th, , AND .

19. Initial Transverse Flow Hubble constant H = 0.25/fm Chojnacki et al.(2005) Positive correlation Hubble-like flow

20. Initial Transverse Flow and Spectra H = 0.02/fm << 0.25/fm Initial flow a.la. Kolb and Rapp(’02) Dissipation in hadron phase also makes p T spectrum hard. (Teaney(’02))  No room for initial flow!? T.H. (’05)  K p CAVEAT: total energy ~ 2*(collision energy) for H=0.25/fm

21. Initial Flow Effect on HBT Radii Hubble const. R out, R long R out /R side ~ 1 for H=0.25 fm -1 SIDE LONG OUT

22. Temperature Distribution at  =6.0 fm/c H=0.02/fm H=0.25/fm

23. Summary The HBT puzzle is still puzzling us (only me?)! Fitting the HBT radii is NOT the solution of the puzzle. Justify parameters after fitting spectra and HBT radii ! Especially, dynamical aspects such as radial flow, source size etc. Dissipative hadronic corona is important to reproduce elliptic flow. However, HBT radii cannot be reproduce by the hybrid model yet.

24. Fitting Parameters by Cramer&Miller Proton p T slope can be reproduced? J.G.Cramer et al.,PRL94,102302(2005)

25. Pion Chemical Potential Partial chemical equilibrium (PCE) T.H. and K.Tsuda(’02)  (T,   ) =(173,123)

26. BONUS SLIDES!

27. Basis of the Announcement Integrated elliptic flow NA49(’03) PHENIX white paper Differential elliptic flow

28. T th <T ch Chemical parameters  particle ratio Thermal parameters  p t spectra Statistical model T ch >T th (conventional) hydro T ch =T th No reproduction of ratio and spectra simultaneously

29. Many people don’t know this… P.Huovinen, QM2002 proceedings

30. Extension of Parameter Space ii Introduction of chemical potential for each hadron! Single T f in hydro Hydro works? Both ratio and spectra?

31. Chemical Potential & EoS EOS Example of chem. potential Partial chemical equilibrium (PCE) Expansion dynamics is changed (or not)? T.H. and K.Tsuda(’02) 

32. Does Dynamics change? Model PCE Model CE Contour(T=const.) T(  ) at origin T.H. and K.Tsuda(’02) (T th ) 

33. p T Spectra How to fix T th in conventional hydro Response to p T slope Spectrum harder with decreasing T th Up to how large p T ? T th independence of slope in chemically frozen hydro No way to fix T th Suggests necessity of (semi)hard components Charged hadrons in AuAu 130AGeV C hemical E quilibrium P artial C hemical E quilibrium T.H. and K.Tsuda (’02)

34. Elliptic Flow T.H. and K.Tsuda (’02) Kolb and Heinz(’04) Is v 2 (p T ) really sensitive to the late dynamics? 0.4 0.6 0.8 0.2 0 0.4 0.6 0.8 0.2 0 1.0 140MeV 100MeV transverse momentum (GeV/c)

35. Mean p T is the Key Slope of v 2 (p T ) ~ v 2 / Response to decreasing T th (or increasing  ) v2v2 PCE CE v 2 / <pT><pT>    Generic feature!

36. Why behaves differently? Simplest case: Pion gas Longitudinal expansion  pdV work! dE T /dy should decrease with decreasing T th.  dN/dy should so. CFO: dS/dy = const.  dN/dy = const.  MUST decreases CE: dS/dy = const.  dN/dy decreases (mass effect)  can increase as long as dN/dy decreases. Result from the 1 st law of thermodynamics & Bjorken flow dE T /dy proper time ideal hydro

37. Are Hydro Results Consistent with Each Other? What does it mean? PHENIX white paper, nucl-ex/0410003 elliptic flow p T spectra p 

38. Summary of Results Models for Hadron Phase v2(pT,m)v2(pT,m) p T spectra Yield or ratio Viscous effect Caveat Chemical Equilibrium Y es Y es *NoNo NoNo * P (Pbar) yields << exp. data Partial Chemical Equilibrium NoNo Y es *Y es NoNo *Only low p T for pions Hadronic Cascade Y es Y es * *Kinetic approach Boundary (QGP  hadron)

39. Finite Mean Free Path & Viscosity See, e.g. Danielewicz&Gyulassy(1985) For ultra-relativistic particles, the shear viscosity is Ideal hydro:  0  shear viscosity  0 Transport cross section

40. FAQ 1.We cannot say “Hydro works very well at RHIC” anymore?  Yes/No. Only a hydro+cascade model does a good job.  Nevertheless, HBT puzzle!  QGP as a perfect fluid. Hadron as a viscous fluid. 2. Why ideal hydro can be used for chemically frozen hydro?  We can show from AND.  One has to distinguish “chemical freeze out” from “chemical non-equilibrium”.

41. Large radial flow reduces v 2 for protons Radial flow pushes protons to high p T regions Low p T protons are likely to come from fluid elements with small radial flow Even for positive elliptic flow of matter, v 2 for heavy particles can be negative in low p T regions! High pT protons Low pT protons x y pTpT Blast wave peak depends on 

42. v 2 (p T ) Stalls in Hadron Phase? D.Teaney(’02) Pb+Pb, SPS 17 GeV, b=6 fm Hadronic rescattering via RQMD does not change v 2 (p T ) for  ! Solid lines are guide to eyes Mechanism for stalling v 2 (p T ) Hydro (chem. eq.): Cancellation between v 2 and  Effect of EoS Hydro+RQMD: Effective viscosity  Effect of finite

43. Summary What have we learned?What have we learned? From hydro+cascade analyses, viscosity is mandatory in the hadron phase: QGP as a perfect fluid and hadrons as a “viscous” fluid. v 2 is sensitive to the early stage of collisions, whereas v 2 (p T ) can also be sensitive to the late stage since v 2 (p T ) is manifestation of interplay between radial flow ( ) and elliptic flow (v 2 ). CommentComment Conventional (chem. equilibrium & ideal) hydro makes full use of neglecting chemical f.o. to reproduce v 2 (p T ) and p T spectra. Accidental reproduction!

44. QGP Fuzzy image if focus is not adjusted yet. QGP QGP Wanna see this? Fine-tune the “hadronic” focus! focus: hadron corona The importance of the dissipative hadronic corona to understand “perfect fluid” sQGP core!