1. 3-D Hydro: present and future Tetsufumi Hirano Columbia University Second RHIC II Science Workshop @ BNL, Probes of EOS

2. Outline Warming up Current Results from ideal hydro Proposal No.1 Revisit of v 2 (p T ) Proposal No.2 Summary

3. Why 3-D Hydro? If one wants to analyze PHOBOS, nucl-ex/0407012 or BRAHMS, PRL88,202301(2002) within hydro, one needs a 3-D hydro since one can assume neither the Bjorken solution nor cylindrical symmetry.

4. Warming Up No. 1 No Boost Invariant Region at RHIC? Basic assumption 1.Finite “Bjorken rod” (-  0 <  s <  0 ) 2.Massless pions 3.Thermal distribution 2020 Space-time rapidity Boost inv. region at RHIC is not ruled out! Don’t mix up  s with y! R Folding Local thermal distributions with the box profile, you get Gaussian-like momentum dist. For details, see Schnedermann, PRC48,2462(’93).

5. Warming Up No.2: v 2 (  ) and v 2 (y) P. Kolb, Heavy Ion Phys.15, 279(2002). Jacobian as an weight fn. Jacobian between y and  Example from 3D hydro v 2 (  ) has a peak even in boost inv. solution. ~10% effect v2v2 dN/d  or dN/dy

6. Results from Ideal Hydro

7. Particle Density Dependence of v 2 Hydrodynamic response is const. v 2 /  ~ 0.2 @ RHIC Exp. data reach hydrodynamic limit at RHIC for the first time. (response)=(output)/(input) Number density per unit transverse area Dimension 2D+boost inv. EoS QGP + hadrons (chem. eq.) Decoupling Sudden freezeout NA49(’03) Kolb, Sollfrank, Heinz (’00) Dawn of the hydro age! Hydro picture only in central collisions???

8. “p T ” Dependence of v 2 “high p T ” “low p T ” Dimension Full 3D (  s coordinate) EoS QGP + hadrons (chem. frozen) Decoupling Sudden freezeout T.H.(’04) particle density low high spatial anisotropy large small Low p T  “Hydrodynamic scaling” High p T  Deviation from hydro scaling. (response)=(output)/(input) Forward region? b~11fm

9. 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)

10. v 2 /  as a function  Dimension Full 3D (  s coordinate) EoS QGP + hadrons (chem. frozen) Decoupling Sudden freezeout No resonance decay T.H.(’05) Caveat 1: v 2 can be reduced by increasing T th in forward region. Caveat 2: Eccentricity can depend on rapidity. Is the hydro scaling seen in v 2 /  (  )? Yes  Forward region ~ Midrapidity with the same particle density No  Nontrivial dynamics in forward region

11. Proposal No.1 Can hydro scaling be seen in forward rapidity AND low p T regions? Need to measure p T of particles in forward rapidity. Doable within current detector? –FTPC at STAR? –Forward Spectrometer at BRAHMS? –PHENIX/PHOBOS? Need detector upgrade/high luminosity?

12. Revisit of v 2 (p T ) T.H. and M.Gyulassy (’05)

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

15. Modeling of Hadron Phase and Freezeout TcTc QGP phase Hadron phase  P artial C hemical E quilibrium EOS Hirano & Tsuda; Teaney; Kolb & Rapp Teaney, Lauret & Shuryak; Bass & Dumitru T ch T th H adronic C ascade C hemical E quilibrium EOS T th Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Ideal hydrodynamics Sudden freezeout: =0  infinity

16. v 2 (p T ) depends on T th Chemical Equilibrium Partial Chemical Equilibrium  K p T.H. and K.Tsuda (’02) Kolb and Heinz(’04) Is v 2 (p T ) really sensitive to the late dynamics? 100MeV 140MeV

17. 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! See next slide!

18. dE T /dy and n/s 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.  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

19. Comments 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 ). Conventional (chem. equilibrium & ideal) hydro makes full use of neglecting chemical f.o. (particle ratios) to reproduce v 2 (p T ) and p T spectra. Accidental reproduction!

20. Can v 2 at Forward Rapidity be Reproduced by Hydro + Cascade ? Dimension 2D+boost inv. EoS Parametrized by latent heat (LH8, LH16, LH-infinity) Hadrons QGP+hadrons (chem. eq.) Decoupling Hybrid (Boltzmann eq.) Teaney, Lauret, Shuryak(’01) Deviation at lower energies can be filled by “viscosity” in hadron gases Latent heat ~0.8 GeV/fm 3 is favored.

21. A hydro + cascade model by Teaney et al. is the only dynamical model to reproduce v 2 and v 2 (p T ) properly. “Viscous” effect is mandatory in the hadron phase The announcement should have been “QGP as a perfect fluid, hadrons as a viscous fluid” !? Summary for Revisit of v 2 (p T )

22. 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.

23. Support Our Phenomenologist! Summary Bulk dynamics in forward region –Hydro scaling (and its violation?) –v 2 /  (  ) or v 2 /  (b) in forward and low p T region. To understand the QGP, we need the transport of hadrons.  3D hydro + hadron cascade We cannot learn anything from data without dynamical analyses.

24. R.Debbie (BRAHMS), proceeding for The 8th Conference on Intersections of Particle And Nuclear Physics (CIPANP2003), New York City, New York (May 19-24, 2003). Blast Wave Fit in Forward Region

25. Centrality Dependence of   CGC >  part,  coll v 2 is 20-25% larger than the others. CGC works well for centrality dependence of multiplicity.

26. QGP Fuzzy image if focus is not adjusted yet. QGP QGP Wanna see this? “fine tuning” of focus! focus: hadron gas