1. Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009 Huichao Song The Ohio State University Supported by DOE 12/14/2009 Lawrence Berkeley National Lab QGP viscosity from RHIC data -- a hydrodynamic perspective Thanks for collaborations and discussions from U. Heinz; Thanks for figures and discussions from K. Dusling, A. El, S. Pratt, Z. Xu, and many others

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

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

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

5. Viscous hydrodynamics S.Bass Conservation laws: - Israel-Stewart eqns.

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

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

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

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

10. Elliptic flow v 2 -both shear & bulk viscosity suppress V 2 at low P T Song & Heinz, 0909 Qualitative effects of & on V 2

11. Shear viscosity & elliptic flow V 2 20-25% v 2 suppression Elliptic flow v 2 - V 2 can be used to extract the QGP shear viscosity -For an acurrate extraction of QGP viscosity, one needs very precise V 2 (experimental data & theoretical results)

12. - V 2 can be used to extract the QGP shear viscosity 20-25% v 2 suppression Elliptic flow v 2 Shear viscosity & elliptic flow V 2 -For an acurrate extraction of QGP viscosity, one needs very precise V 2 (experimental data & theoretical results)

13. - V 2 can be used to extract the QGP shear viscosity 20-25% v 2 suppression - 10% uncertainties in V 2 translate into 50% uncertainties for the extracted value of Elliptic flow v 2 Example: If v 2 is increased by 10%, one need to increase by in order to describe the same exp. data Shear viscosity & elliptic flow V 2 -For an acurrate extraction of QGP viscosity, one needs very precise V 2 (experimental data & theoretical results)

14. Extracting from V 2 data Input / parameters for viscous hydro -initial conditions: -EoS: EOS Q, EOS L, EOS L + chemical non-equil. HRG EOS -treatment of hadronic stage and freeze-out procedure: -viscosities & relaxation times: -initial eccentricity (Glauber/CGC ; optical/fluctuations) -initialization for

15. Effects of initial eccentricity on Luzum & Romatschke, PRC 2008 GlauberCGC -event by event fluctuations: talk by A. Dumitru -Glauber vs.CGC: ~20-30% effect on ~100% uncertainties on

16. Luzum & Romatschke, PRC 2008 GlauberCGC -Effects from highly viscous & non-chemical equilibrium hadronic stage, bulk viscosity … Effects of initial eccentricity on NOT so fast !

17. Extracting from V 2 data Input / parameters for viscous hydro -initial conditions: -EoS: -treatment of hadronic stage and freeze-out procedure: -viscosities & relaxation times: -initial eccentricity -chemical composition of HRG -effects of highly viscous HRG -initialization for shear and bulk pressure

18. Effects of chemical composition of HRG on 30% PCE vs.CE (HRG) Ideal hydro P. Huovinen 07 -PCE EoS vs. CE EoS (ideal hydro): change v 2 by ~30% Partial Chemical Equilibrium (PCE) vs. Chemical Equilibrium (CE)

19. 30% PCE vs.CE (HRG) -Constraining requires: a proper description of partial chemical equilibrium in HRG Glauber CGC 30% P. Huovinen 07 Luzum &Romatschke 08 Effects of chemical composition of HRG on -PCE EoS vs. CE EoS (ideal hydro): change V 2 ~30% influence ~100% Ideal hydro

20. Effects of highly viscous hadronic stage on -highly viscous hadronic stage: change V 2 ~30-50% influence ~100-150% -need viscous hydro + hadron cascade hybrid approach 30-50% T. Hirano Ideal hydro

21. Extracting from V 2 data Input / parameters for viscous hydro -initial conditions: -EoS: (EOSQ vs EOSL) -treatment of hadronic stage and freeze-out procedures: -viscosities & relaxation times: -initial eccentricity -chemical composition of HRG -viscosity of HRG -initialization for shear and bulk pressure

22. talk by P. Houvinen Effects from softness of EOS 40% 30% Song & Heinz PRC 08 -- EOS L: Katz 05 lattice data for QGP SM-EOS Q vs. EOS L --more realistic EOS for hydro -- softness of EOS: ~5-10% effects on V 2 ~25% uncertainties on + CE EOS for HRG 0903 lattice data for QGP + PCE EOS for HRG

23. Extracting from V 2 data Input / parameters for viscous hydro -initial conditions: -EoS: (EOSQ vs EOSL) -treatment of hadronic stage and freeze-out procedures: -viscosities & relaxation times: -initial eccentricity -chemical composition of HRG -viscosity of HRG -initialization for shear and bulk pressure

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

25. Extracting from V 2 data Input / parameters for viscous hydro -initial conditions: -EoS: (EOSQ vs EOSL) -treatment of hadronic stage and freeze-out procedures: -initial eccentricity -chemical composition of HRG -viscosity of HRG -effects from bulk viscosity - shear pressure: relaxation times and initialization

26. QGPHRG bulk viscosity and relaxation time Bulk viscosity: Relaxation times: also peaks near T c, this plays an important role for bulk viscous dynamics

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

28. QGPHRG bulk viscosity and relaxation time Bulk viscosity: Relaxation times: also peaks near T c, N-S initialization: viscous hydro breaks down ( ) for larger viscous hydro is only valid with small small bulk viscous effects on V 2 large near T c keeps large negative value of in phase transition region this plays an important role for bulk viscous dynamics

29. Uncertainties from bulk viscosity N-S initializationZero initialization -with a critical slowing down, effects from bulk viscosity effects are much smaller than from shear viscosity bulk viscosity influences V 2 ~5% (N-S initial.) <4% (zero initial.) Song & Heinz, 0909 uncertainties to ~20% (N-S initial.) <15% (zero initial.)

30. Extracting from RHIC data --the current status of viscous hydrodynamics -initial conditions: CGC vs. Glauber ~20-30% -EoS: EOS Q, vs. EOS L ~5- 10% -chemical composition of HRG : (PEC vs. CE) ~30% -viscosity of HRG (or equil. HRG vs. non-equil. HRG) : ~30-50% -bulk viscosity: ~5% (uncertainties in V 2 )

31. Extracting from RHIC data --the current status of viscous hydrodynamics GlauberCGC Luzum & Romatschke, PRC 2008 -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% (uncertainties in ) conservative upper limit:

32. Extracting from RHIC data --the current status of viscous hydrodynamics GlauberCGC Luzum & Romatschke, PRC 2008 -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% (uncertainties in ) conservative upper limit: Can we further increase the accuracy of extracted ? YES ! recent progress: Heinz et al. 0907

33. Extracting from RHIC data --the current status of viscous hydrodynamics GlauberCGC Luzum & Romatschke, PRC 2008 -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% (uncertainties in ) conservative upper limit: recent progress: Heinz et al. 0907 -To further decrease the uncertainties from bulk viscosity, (or to extract both shear & bulk viscosity from exp. data), one need more sensitive exp. observables

34. other observables that are sensitive to - v 2 /ε: dependence on system size & shear viscosity -photon spectra -HBT radii … …

35. Song & Heinz PRC 08 -larger shear viscous suppression of elliptic flow in smaller systems System size dependence of shear viscous effects

36. Song & Heinz PRC 08 System size dependence of shear viscous effects -the slope of the multiplicity scaling of v 2 /ε is sensitive to the value of shear viscosity -larger shear viscous suppression of elliptic flow in smaller systems

37. Song & Heinz PRC 08 System size dependence of shear viscous effects -larger shear viscous suppression of elliptic flow in smaller systems -the slope of the multiplicity scaling of v 2 /ε is sensitive to the value of shear viscosity

38. Song & Heinz PRC 08 System size dependence of shear viscous effects -larger shear viscous suppression of elliptic flow in smaller systems -the slope of the multiplicity scaling of v 2 /ε is sensitive to the value of shear viscosity

39. Multiplicity scaling of v 2 /ε Song & Heinz PRC 08 -to reproduce the experimental data (slope), a constant is not enough! -the slope of the multiplicity scaling of v 2 /ε is sensitive to the value of shear viscosity

40. Multiplicity scaling of v 2 /ε Song & Heinz PRC 08 -to reproduce the experimental data (slope), a constant is not enough! -the slope of the multiplicity scaling of v 2 /ε is sensitive to the value of shear viscosity -data indicate: smaller viscous effects in QGP; larger viscous effects in HRG -need viscous hydro + hadron cascade hybrid approach or inputting

41. other observables that are sensitive to -photon spectra -HBT radii … … - v 2 /ε: dependence on system size & shear viscosity

42. EM probes: Photons Pion spectra -Viscous hardening of P T -spectra is stronger for photons than hadrons K. Dusling, 0903 Photon spectra -Photon spectra MAY HELP to constrain the 2-d range of QGP viscosity & thermalization time, together with other observables ( V 2 …) -However, earlier thermalization also leads to harder photon spectra (Dusling 0903)

43. other observables that are sensitive to -photon spectra -HBT radii … … - v 2 /ε: dependence on system size & shear viscosity

44. HBT radii - is sensitive to the QGP viscosity - HBT HELPS to constrain the QGP viscosity, together with other observables ( V 2 …) S. Pratt QM09 with viscosity without viscosity - However, viscosity is only one of the many ingredients that affect HBT radii (Pratt QM09)

45. Recent theroetical developments in viscous hydrodynamics (MSU, Frankfurt, Krakow, etc) - 3+1-d viscous hydro: Several groups are working on it - in multi-component systems - 3 rd order viscous hydrodynamics Talk by A. El Talk by G. Denicol Talk by D.Teaney and D. Molnar - P T -dependent of viscous modification of the particle distributions

46. A short summary BUT: to extract QGP viscosity, one must consider (at least) all the following aspects: - a realistic EOS: EOS L vs. SM-EOS Q, PCE vs. CE - initial conditions: CGC vs. Glauber initialization, optical vs. fluctuations - bulk viscosity: uncertainties from bulk viscosity … … - hadronic stage : viscous hydro+ hadron cascade - is sensitive to A first attempt to constrain from RHIC data indicates

47. Thank You

48. EOS

49. Elliptical flow v 2 -v 2 is sensitive to viscosity, especially shear viscosity Qualitative effects of & on V 2 Change the flow profile during hydro evolution Flow + spectra correc. Spectra correc.: viscous hydro (shear only) ideal hydro viscous hydro (bulk only) (with only flow correction here) A. Monnai talk : spectra correc. for bulk viscosity Song & Heinz, 0909

50. EM probes: Photons -Photon spectra are more sensitive to QGP shear viscosity than hadrons Photon spectra -Photon spectra may HELP to constrain QGP shear viscosity and hydro starting time -Photon spectra are also sensitive to hydro starting time -More sophisticated theoretical modeling in the future: including photon emitted from hadronic stage with modified photon emission rate, etc ; better experimental data K. Dusling, 0903

51. -To describe the experimental data, one need to consider the contribution from all kinds of aspects besides shear viscosity S. Pratt QM09

52. -Heinz, Moreland and Song the effects from different initializations

53. -Heinz, Moreland and Song the effects from different initializations

54. Glauber CGC

55. Glauber CGC