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What did we learn from v 2 ( p T ; m ) at RHIC?

What did we learn from v 2 ( p T ; m ) at RHIC?. Tetsufumi Hirano and Miklos Gyulassy. The Berkeley School, LBNL, CA, May 19, 2005. Basis of the Announcement. PHENIX white paper. NA49(’03). Integrated elliptic flow. Differential elliptic flow. Purposes of this talk

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What did we learn from v 2 ( p T ; m ) at RHIC?

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  1. What did we learn fromv2(pT; m) at RHIC? Tetsufumi Hirano and Miklos Gyulassy The Berkeley School, LBNL, CA, May 19, 2005

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

  3. Purposes of this talk • To clarify the origin of difference among hydro results • To claim the importance of viscous effects in the hadron phase (“Dissipative Hadronic Corona”) Are Hydro Results Consistentwith Each Other? What does it mean? p p elliptic flow PHENIX white paper, nucl-ex/0410003 pT spectra

  4. Modeling of Hadron Phase and Freezeout Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Hirano & Tsuda; Teaney; Kolb & Rapp Teaney, Lauret & Shuryak; Bass & Dumitru T ~1 fm/c QGP phase Ideal hydrodynamics Tc ~3 fm/c Chemical Equilibrium EOS Partial Chemical Equilibrium EOS Tch Hadronic Cascade Hadron phase Tth Tth ~10-15 fm/c t Sudden freezeout: l=0infinity

  5. 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

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

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

  8. 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

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

  10. 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

  11. Elliptic Flow Kolb and Heinz(’04) Is v2(pT) really sensitive to the late dynamics? 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)

  12. Mean pT is the Key Generic feature! t t Slope of v2(pT) ~ v2/<pT> Response todecreasing Tth (or increasing t) v2 <pT> v2/<pT> CE PCE t

  13. Cancel between v2 and <pT> v2(pT) Chemical Eq. v2(pT) v2 Tth t v2 <pT> pT v2(pT) Chemical F.O. <pT> pT v2 <pT> pT

  14. 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

  15. Are Hydro Results Consistentwith Each Other? What does it mean? p p elliptic flow PHENIX white paper, nucl-ex/0410003 pT spectra

  16. Summary of Results

  17. Summary • 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. • v2 is sensitive to the early stage of collisions, whereas v2(pT) can also be sensitive to the late stage since v2(pT) is manifestation of interplay between radial flow (<pT>) and elliptic flow (v2). • Comment • Conventional (chem. equilibrium & ideal) hydro makes full use of neglecting chemical f.o. to reproduce v2(pT) and pT spectra. Accidental reproduction!

  18. 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!

  19. BONUS SLIDES!

  20. 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

  21. 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”.

  22. Today’s Breaking News May 19 2005 The Berkeley Tribune Ideal hydrodynamics with chemical equilibrium “accidentally” reproduces transverse momentum dependence of the elliptic flow at RHIC. (T.H.)

  23. 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!

  24. 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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