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What can we learn from hydrodynamic analysis of elliptic flow?

Quark Matter 2005, August 4-9, Budapest, Hungary. What can we learn from hydrodynamic analysis of elliptic flow?. Tetsufumi Hirano Dept. of Physics, Columbia Univ. T.H. and M.Gyulassy, nucl-th/0506049 T.H., Y.Nara et al ., work in progress. Outline.

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What can we learn from hydrodynamic analysis of elliptic flow?

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  1. Quark Matter 2005, August 4-9, Budapest, Hungary What can we learn from hydrodynamic analysis of elliptic flow? Tetsufumi Hirano Dept. of Physics, Columbia Univ. T.H. and M.Gyulassy, nucl-th/0506049 T.H., Y.Nara et al., work in progress.

  2. Outline • Perfect fluidity of sQGP core and highly dissipative hadronic corona • CGC + full 3D hydro + cascade • Hydrodynamic analysis suggests even a signal of DECONFINEMENT?!

  3. Our claims: • Ideal hydrodynamics accidentally reproduces these data! • Nevertheless, “perfect fluidity of the sQGP” statement and early thermalization still hold. • WHY!!!??? Bases of the Discovery PHENIX white paper NA49(’03) Integrated elliptic flow Differentialelliptic flow

  4. Classification of Hydro Models Model CE: Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Model PCE: Hirano & Tsuda; Teaney; Kolb & Rapp… Model HC: Teaney, Lauret & Shuryak; Bass & Dumitru… T ~1 fm/c QGP phase Perfect Fluid of QGP Tc ~3 fm/c Chemical Equilibrium EOS Partial Chemical Equilibrium EOS Tch Hadronic Cascade Hadron phase Tth Tth ~10-15 fm/c t ideal hydrodynamics

  5. Are hydro results consistent?If not, what does it mean? p p PartialCE elliptic flow HadronicCascade Chem.Eq. PHENIX white paper, NPA757,184(2005) pT spectra

  6. Differential Elliptic Flow Developsin the Hadron Phase? Kolb and Heinz(’04) 100MeV T.H. and K.Tsuda (’02) 140MeV 0.8 1.0 0.2 0.6 0 0.4 0.8 0.2 0.6 0 0.4 transverse momentum (GeV/c)

  7. Mean pT is the Key t t Response todecreasing Tth (or increasing t) v2 <pT> v2/<pT> CE PCE

  8. Cancel between v2 and <pT> v2(pT) v2(pT) At hadronization Chemical Eq. v2 v2 freezeout <pT> <pT> pT pT v2(pT) Chemical F.O. CE: increase CFO: decrease v2 <pT> pT

  9. 1.Why mean pT behaves so differently?2. Why CE result ~ HC result? PartialCE HadronicCascade PHENIX white paper, NPA757,184(2005) Chem.Eq.

  10. For a more rigorous discussion, see T.H. and M.Gyulassy, nucl-th/0506049 Intuitive Picture Mean ET decreases due to pdV work Chemical Freezeout • ETper particle increases • in chemical equilibrium. • This effect delays cooling of the system like a viscous fluid. • Chemical equilibrium imitates viscosity at the cost of particle yield!!! MASS energy KINETIC energy Chemical Equilibrium

  11. Summary of Hydro Results “No-Go theorem” Ruled out! WINNER for hydro race at RHIC !  Hybrid model (Ideal QGP fluid + dissipative hadron gas)

  12. CGC + Full 3D Hydro + Cascade t Hadronic Corona (Cascade) sQGP core (Full 3D Hydro) z 0 Color Glass Condensate

  13. CGC + Full 3D Hydro + Hadronic Cascade PHOBOS data: “Triangle shape” prop. to dN/dh Tth=100MeV: “Trapezoidal shape” Typical hydro result Tth=169MeV: Triangle shape!Just after hadronization CGC+hydro+cascade: Good agreement! Perfect fluid sQGP core + dissipative hadronic corona picture works as well in forward region!

  14. What Have We Learned? h : shear viscosity, s : entropy density T.H. and M.Gyulassy (’05) • Absolute value of viscosity • Its ratio to entropy density ! What makes this sudden behavior? DECONFINEMENT

  15. Conclusion • Critical data harvested at RHIC • Particle ratio (Particle yield) • pT spectra • v2, v2(pT), and v2(h) Hydrodynamic analyses Nearly perfect fluidity of the sQGP core AND Highly dissipative hadronic corona  DECONFINEMENT!?

  16. BONUS SLIDES!

  17. Tth<Tch • Statistical model • Tch>Tth • (conventional) hydro • Tch=Tth • No reproduction • of ratio and spectra • simultaneously Chemical parameters  particle ratio Thermal parameters pt spectra

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

  19. Extension of Parameter Space • Single Tf in hydro • Hydro works? • Both ratio and • spectra? Introduction of chemical potential for each hadron! mi

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

  21. Does Dynamics change? Contour(T=const.) T(t) at origin Model CE <vr>(Tth) Model PCE T.H. and K.Tsuda(’02) t

  22. pT Spectra • How to fix Tth in conventional hydro • Response to pT slope • Spectrum harder with decreasing Tth • Up to how large pT? Chemical Equilibrium T.H. and K.Tsuda (’02) Partial Chemical Equilibrium • Tth independence of slope in chemically frozen hydro • No way to fix Tth • Suggests necessity of • (semi)hard components Charged hadrons in AuAu 130AGeV

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

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

  25. The End of 50-Year-Old Ideal, Chem. Eq. Hadronic Fluid After the famous Landau’s paper (1953), ideal and chemical equilibrium hadronic hydrodynamics has been exploited for a long time. However, the model may not be used when chemical freezeout happens earlier than thermal freezeout since it accidentally reproduces pT spectra and v2(pT) at the cost of particle yields.

  26. Digression A Long Long Time Ago… …we obtain the value R (Reynolds number)=1~10… Thus we may infer that the assumption of the perfect fluid is not so good as supposed by Landau.

  27. Check Sheet for Prevailing Opinion 1. Ideal hydrodynamics reproduce v2(pT) remarkably well, but not HBT radii. TRUE FALSE X TRUE: Ideal Hydrodynamics reproduces neither v2(pT) nor HBT radii at RHIC. 2. v2(pT) is not sensitive to the late hadronic stage. TRUE FALSE X TRUE: v2(pT) depends on thermal equilibrium, chemical equilibrium, and viscous effects in the hadron phase.

  28. FAQ • 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”.

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

  30. Toward a Unified Model in H.I.C.T.H. and Y.Nara (’02-) 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? Not covered in this talk Hydrodynamics (full 3D hydro) Parton energy loss (a la Gyulassy-Levai-Vitev) Jet quenching QGP Hadron gas Hadronic cascade (JAM) Recombination Fragmentation Proper time Low pT Intermediate pT High pT

  31. Importance of Thermalization Stage at RHIC • CGC + hydro + cascade • agreement only up to • 15~20% centrality • (impact parameter ~5fm) • Centrality dependence • of thermalization time • Semi-central to peripheral collisions: • Not interpreted only by hadronic dissipation • Important to understand pre-thermalization stage

  32. Initial Eccentricity CGC initial condition gives ~25% larger initial eccentricity than participant or binary collision scaling.

  33. Viscosity and Entropy • Reynolds number R>>1 Perfect fluid where • 1+1D Bjorken flow (Ideal) (Viscous) h : shear viscosity (MeV/fm2) s : entropy density (1/fm3) h/s is a good dimensionless measure to see viscous effects.

  34. Large radial flow reduces v2 for protons Blast wave peak depends on f High pT protons x y pT • 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!

  35. 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.): • Cancellation between • v2 and <pT> • 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

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