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3 rd Asian Triangle Heavy-Ion Conference (ATHIC 2010) October 18-20, 2010

Viscous hydrodynamics and the extraction of ( η /s) QGP from heavy-ion collision data*. Ulrich Heinz. 3 rd Asian Triangle Heavy-Ion Conference (ATHIC 2010) October 18-20, 2010. In collaboration with Huichao Song, Shen Chun, Pasi Huovinen , Scott Moreland, and Tetsu Hirano.

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3 rd Asian Triangle Heavy-Ion Conference (ATHIC 2010) October 18-20, 2010

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  1. Viscous hydrodynamics and the extraction of (η/s)QGP from heavy-ion collision data* Ulrich Heinz 3rd Asian Triangle Heavy-Ion Conference (ATHIC 2010) October 18-20, 2010 In collaboration with Huichao Song, Shen Chun, PasiHuovinen, Scott Moreland, and Tetsu Hirano *Supported by DOE and CERN 08/16/2010

  2. What is viscosity? Shear viscosity – measures the resistance to flow gradients acts against the buildup of flow anisotropy Bulk viscosity – measures the resistance to expansion acts against the buildup of radial flow Heat conductivity – measures the ability of heat transfer Assume: (RHIC&LHC)

  3. Ideal hydrodynamics hydro S.Bass Conservation laws: ideal hydro: local equilibrium - 4 equations - 5 unknowns Input: “EOS” -EOS is one of the important factors that influence the expansion of system harder EOS (with larger ) faster expansion

  4. Viscous hydrodynamics hydro S.Bass Conservation laws: ideal hydro: local equilibrium viscous hydro: near equilibrium shear pressure tensor bulk pressure:

  5. Viscous hydrodynamics hydro S.Bass Conservation laws: - Israel-Stewart eqns. (+ additional second order terms on r.h.s., see D. Rischke’s talk)

  6. Viscous hydrodynamics hydro S.Bass Conservation laws: - Israel-Stewart eqns. viscous hydro: near-equilibrium system pre-equilibrium dynamics + viscous hydro+ hadron cascade Initial conditions final conditions

  7. Viscous hydrodynamics Input: “EOS” hydro S.Bass Conservation laws: - Israel-Stewart eqns. initial and final conditions Bjorken appro. : reduces (3+1)-d hydro to (2+1)-d hydro

  8. Qualitative effects of & on spectra The same initial & final conditions: ideal hydro viscous hydro-shear only viscous hydro-bulk only spectra Song & Heinz, 0909 -shear viscosity: flatter spectra -bulk viscosity: steeper spectra

  9. Qualitative effects of & on spectra The same initial & final conditions: ideal hydro viscous hydro-shear only viscous hydro-bulk only spectra radial flow Song & Heinz, 0909 -shear viscosity: flatter spectra; increases radial flow -bulk viscosity: steeper spectra; decreases radial flow

  10. Qualitative effects of & on V2 Elliptic flow v2 Song & Heinz, 0909 - both shear & bulk viscosity suppress v2at low pT

  11. Shear viscosity & elliptic flow v2 Elliptic flow v2 20-25% v2 suppression - v2can be used to extract the QGP shear viscosity • for an accurate extraction of QGP viscosity, one needs very precise v2 • (experimental data & theoretical results)

  12. Shear viscosity & elliptic flow v2 Elliptic flow v2 20-25% v2 suppression -v2 can be used to extract the QGP shear viscosity • for an accurate extraction of QGP viscosity, one needs very precise v2 • (experimental data & theoretical results)

  13. Shear viscosity & elliptic flow v2 Elliptic flow v2 20-25% v2 suppression Example:If v2is increased by 10%, one needs to increase by in order to describe the same exp. data -10%uncertainties in V2 translate into 50% uncertainties for the extracted value of - v2 can be used to extract the QGP shear viscosity • for an accurate extraction of QGP viscosity, one needs very precise v2 • (experimental data & theoretical results)

  14. Extracting from v2 data Input / parameters for viscous hydro - initial conditions: - initial eccentricity (Glauber vs. CGC ; optical vs. fluctuating) - treatment of hadronic stage and freeze-out procedure - EoS: EOS Q, EOS L, EOS L + chemical non-equilibrium HRG EOS - viscosities & relaxation times: - initialization for

  15. Effect of initial eccentricity on v2 Glauber Luzum & Romatschke, PRC 2008 CGC - Glauber vs.CGC: ~20-30% effect on v2~100% uncertainty on

  16. Effect of initial eccentricity on v2 Glauber Luzum & Romatschke, PRC 2008 CGC NOT so fast ! - Effects fromhighly viscous & non-chemical equilibrium hadronic stage, bulk viscosity …

  17. Event-averaged eccentricity from fluctuating initial conditions Scott Moreland et al., PRC80 (‘09) 061901

  18. Extracting from v2 data Input / parameters for viscous hydro - initial conditions: - initial eccentricity - treatment of hadronic stage and freeze-out procedure: - chemical composition of HRG - effects of highly viscous HRG - EoS: - viscosities & relaxation times: - initialization for shear and bulk pressure

  19. Effect of HRG chemical composition on v2 Partial Chemical Equilibrium (PCE) vs. Chemical Equilibrium (CE) PCE vs.CE (HRG) Ideal hydro 30% P. Huovinen 07 - PCE EoS vs. CE EoS (ideal hydro): changes v2 by ~30%

  20. Effects of HRG chemical composition on v2 PCE vs.CE (HRG) Glauber Ideal hydro 30% 30% CGC P. Huovinen 07 Luzum &Romatschke 08 - PCE EoS vs. CE EoS (ideal hydro): changes v2~30%influences ~100% - Constraining requires: a proper description of partial chemical equilibrium in HRG

  21. Effects of highly viscous hadronic stage on v2 Ideal hydro 30-50% T. Hirano - highly viscous hadronic stage: changes v2~30-50% influences ~100-150% - need viscous hydro + hadron cascade hybrid approach

  22. Extracting from v2 data Input / parameters for viscous hydro - initial conditions: - initial eccentricity - treatment of hadronic stage and freeze-out procedures: - chemical composition of HRG - viscosity of HRG - EoS: EOS Q vs. EOS L vs. s95p-PCE - viscosities & relaxation times: - initialization for shear and bulk pressure

  23. EOS SM-EOS Q: Slightly smoothed first-order phase transition, HRG in chemical equilibrium EOS L: Rapid crossover, older lattice data, HRG in chemical equilibrium s95p-PCE: latest lattice QCD data at high T matched to chemically frozen HRG at low temperature (PasiHuovinen & Peter Petreczky) SM-EOS Q EOS L s95p-PCE Note: s95p-PCE has no “softest point”!

  24. EOS dependence of hadron spectra Chun Shen et al. (2010) • s95p-PCE produces less radial flow than other EoSs, by making the fireball decouple sooner • O(10%) effects of EoS on v2 • Shear viscosity helps to add radial flow but suppresses v2 • Proton spectra prefer larger η/s, charged hadron v2 prefers smaller η/s.

  25. Extracting from v2 data Input / parameters for viscous hydro - initial conditions: - initial eccentricity - treatment of hadronic stage and freeze-out procedures: - chemical composition of HRG - viscosity of HRG - EoS: (EOSQ vs EOSL) - shear pressure: relaxation times and initialization - effects from bulk viscosity

  26. bulk viscosity and relaxation time Bulk viscosity: Relaxation times: also peaks near Tc, this plays an important role for bulk viscous dynamics HRG QGP

  27. bulk viscosity and relaxation time Bulk viscosity: Relaxation times: also peaks near Tc, this plays an important role for bulk viscous dynamics HRG QGP Zero initialization: large near Tc prevents from growing to large values suppresses bulk viscous effects

  28. bulk viscosity and relaxation time Bulk viscosity: Relaxation times: also peaks near Tc, this plays an important role for bulk viscous dynamics HRG QGP N-S initialization: large near Tckeeps large negative value of in phase transition region viscous hydro breaks down ( ) for larger viscous hydro is only valid with small small bulk viscous effects on v2

  29. Uncertainties from bulk viscosity N-S initialization Zero initialization Song & Heinz, 0909 • with critical slowing down of , effects from bulk viscosity are much • smaller than from shear viscosity bulk viscosity influences v2~5% (N-S initial.)<4% (zero initial.) uncertainties to ~20% (N-S initial.) <15% (zero initial.)

  30. Extracting from RHIC data --the current status of viscous hydrodynamics (uncertainties in v2) -initial conditions: CGC vs. Glauber~20-30% -EoS: EOS Q vs. EOS L ~5-10% -chemical composition of HRG : (PCE vs. CE) ~30% -viscosity of HRG (or equil. HRG vs. non-equil. HRG): ~30-50% -bulk viscosity:~5%

  31. Luzum & Romatschke, PRC 2008 Glauber CGC Extracting from RHIC data --the current status of viscous hydrodynamics (uncertainties in ) -initial conditions: CGC vs. Glauber~100% -EoS: EOS Q, vs. EOS L ~25% -chemical composition of HRG : (PEC vs. CE) ~100% -viscosity of HRG (or equil. HRG vs. non-equil. HRG): ~100-150% -bulk viscosity: ~20% conservative upper limit:

  32. Luzum & Romatschke, PRC 2008 Glauber CGC Extracting from RHIC data --the current status of viscous hydrodynamics (uncertainties in ) - initial conditions: CGC vs. Glauber~100% ?? - EoS: EOS Q, vs. EOS L ~25% - chemical composition of HRG : (PEC vs. CE) ~100% - viscosity of HRG (or equil. HRG vs. non-equil. HRG): ~100-150% - bulk viscosity: ~20% conservative upper limit: YES ! Can we further increase the accuracy of extracted?

  33. A hybrid approach: VISH2+1 ∩ H2O ∩ UrQMD H. Song, S. Bass, UH, T. Hirano, C. Shen (2010), in preparation PHOBOS ‘08 Switching temperature Tsw=160 MeV.

  34. A hybrid approach: VISH2+1 ∩ H2O ∩ UrQMD H. Song, S. Bass, UH, T. Hirano, C. Shen (2010), in preparation

  35. A short summary - v2 is sensitive to A first attempt to constrain from RHIC data, incorporating most of the important physics, indicates BUT additional systematic studies necessary: • initial conditions: CGC vs. Glauber initializations – can we get a handle • on the initial eccentricity?!? • - pre-equilibrium flow: match pre-equilibrium models to viscous hydro - bulk viscosity: uncertainties from bulk viscosity? - hadronic stage: safe window for switching from VISH to UrQMD? • H2O conversion: viscous correction to distribution function at Tsw • e-by-e hydro: should propagate fluctuating initial state event-by-event • through viscous hydro (Schenke et al. 2010), perform • average over events only at the end … … … …

  36. Thank you!

  37. Effects from softness of EOS 40% 30% Song & Heinz PRC 08 SM-EOS Q vs. EOS L −softness of EOS: ~5-10% effects on v2~25%uncertainties on − EOS L: Katz 05 lattice data for QGP + CE EOS for HRG in progress (with Shen Chun & PasiHuovinen): − more realistic EOS for hydro 0903 lattice data for QGP + PCE EOS for HRG

  38. Extracting from v2 data Input / parameters for viscous hydro - initial conditions: - initial eccentricity - treatment of hadronic stage and freeze-out procedures: - chemical composition of HRG - viscosity of HRG - EoS: EOSQ vs EOSL vs. s95p-PCE - viscosities & relaxation times: - initialization for shear and bulk pressure

  39. - v2 is insensitive to initializations of and relaxation time ! shear pressure: relaxation times & initialization Song, Ph.D thesis (since is short) - when extracting : one can neglect the uncertainties from & initialization of

  40. Qualitative effects of & on v2 ideal hydro Elliptical flow v2 Song & Heinz, 0909 viscous hydro (shear only) change of flow profile during hydro evolution flow + spectra correction spectra correction: viscous hydro (bulk only) (with only flow correction here) A. Monnai talk : spectra correc. for bulk viscosity - v2 is sensitive to viscosity, especially shear viscosity

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