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3-D Hydro: present and future

This text discusses the importance of 3-D hydrodynamics in analyzing PHOBOS and BRAHMS experiments and presents current results from ideal hydrodynamics. It also outlines proposals for further research and explores the factors affecting elliptic flow and particle density in different regions.

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3-D Hydro: present and future

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  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 v2(pT) • Proposal No.2 • Summary

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

  4. Warming Up No. 1No Boost Invariant Region at RHIC? • Basic assumption • Finite “Bjorken rod” (-h0<hs<h0) • Massless pions • Thermal distribution R 2h0 Space-time rapidity Folding Local thermal distributions with the box profile, you get Gaussian-like momentum dist. For details, see Schnedermann, PRC48,2462(’93). Boost inv. region at RHIC is not ruled out! Don’t mix up hs with y!

  5. Warming Up No.2: v2(h) and v2(y) Jacobian as an weight fn. P. Kolb, Heavy Ion Phys.15, 279(2002). dN/dh or dN/dy v2 ~10% effect Jacobian between y and h Example from 3D hydro v2(h) has a peak even in boost inv. solution.

  6. Results from Ideal Hydro

  7. Particle Density Dependence of v2 NA49(’03) Kolb, Sollfrank, Heinz (’00) • Dimension • 2D+boost inv. • EoS • QGP + hadrons (chem. eq.) • Decoupling • Sudden freezeout (response)=(output)/(input) • Hydrodynamic response is • const. v2/e ~ 0.2 @ RHIC • Exp. data reach hydrodynamic • limit at RHIC for the first time. Number density per unit transverse area Dawn of the hydro age! Hydro picture only in central collisions???

  8. “pT” Dependence of v2 T.H.(’04) • Dimension • Full 3D(t-hs coordinate) • EoS • QGP + hadrons (chem. frozen) • Decoupling • Sudden freezeout “high pT” (response)=(output)/(input) “low pT” b~11fm • Low pT“Hydrodynamic scaling” • High pTDeviation from hydro scaling. particle density low high Forward region? spatial anisotropy large small

  9. 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

  10. v2/e as a function h T.H.(’05) • Dimension • Full 3D(t-hs coordinate) • EoS • QGP + hadrons (chem. frozen) • Decoupling • Sudden freezeout • No resonance decay Caveat 1: v2 can be reduced by increasing Tth in forward region. Caveat 2: Eccentricity can depend on rapidity. • Is the hydro scaling seen in v2/e(h)? • 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 pT regions? • Need to measure pT 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 v2(pT) T.H. and M.Gyulassy (’05)

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

  14. Modeling of Hadron Phase and Freezeout Kolb, Sollfrank, Huovinen & Heinz; Hirano;… Hirano & Tsuda; Teaney; Kolb & Rapp Teaney, Lauret & Shuryak; Bass & Dumitru Ideal hydrodynamics QGP phase Tc Chemical Equilibrium EOS Partial Chemical Equilibrium EOS Tch Hadronic Cascade Hadron phase Tth Tth t Sudden freezeout: l=0infinity

  15. v2(pT) depends on Tth Partial Chemical Equilibrium Chemical Equilibrium p 140MeV Kolb and Heinz(’04) 100MeV K p Is v2(pT) really sensitive to the late dynamics? T.H. and K.Tsuda (’02)

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

  17. dET/dy and n/s Simplest case: Pion gas Longitudinal expansion  pdV work! dET/dy ideal hydro proper time • CFO: dS/dy = const. • dN/dy = const. • <pT> 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

  18. Comments • 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). • Conventional (chem. equilibrium & ideal) hydro makes full use of neglecting chemical f.o. (particle ratios) to reproduce v2(pT) and pT spectra. Accidental reproduction!

  19. Can v2 at Forward Rapidity be Reproduced by Hydro + Cascade ? Teaney, Lauret, Shuryak(’01) • Dimension • 2D+boost inv. • EoS • Parametrized by latent heat • (LH8, LH16, LH-infinity) • Hadrons • QGP+hadrons (chem. eq.) • Decoupling • Hybrid (Boltzmann eq.) • Deviation at lower energies can be filled by “viscosity” in hadron gases • Latent heat ~0.8 GeV/fm3 is favored.

  20. Summary for Revisit of v2(pT) A hydro + cascade model by Teaney et al. is the only dynamical model to reproduce v2 and v2(pT) properly. “Viscous” effect is mandatory in the hadron phase The announcement should have been “QGP as a perfect fluid, hadrons as a viscous fluid” !?

  21. 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.

  22. Summary • Bulk dynamics in forward region • Hydro scaling (and its violation?) • v2/e(h) or v2/e(b) in forward and low pT region. • To understand the QGP, we need the transport of hadrons.  3D hydro + hadron cascade • We cannot learn anything from data without dynamical analyses. Support Our Phenomenologist!

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

  24. Centrality Dependence of e CGC works well for centrality dependence of multiplicity. eCGC> epart, ecoll v2 is 20-25% larger than the others.

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

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