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Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009

Understand the measures and influences of shear and bulk viscosity, heat conductivity, and equation of state (EOS) on QGP expansion from RHIC and LHC data. Explore ideal hydrodynamics, near-equilibrium systems, and their effects on radial and elliptic flow spectra. Extract accurate QGP viscosity values from V2 data using precise experimental and theoretical results.

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Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009

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  1. QGP viscosity from RHIC data -- a hydrodynamic perspective Huichao Song The Ohio State University Lawrence Berkeley National Lab Joint CATHIE/TECHQM Workshop, BNL, Dec 14-18, 2009 Supported by DOE 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 12/14/2009

  2. What is viscosity Shear viscosity – measures the resistance to flow gradients act against the buildup of flow anisotropy Bulk viscosity – measures the resistance to expansion act 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.

  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 V2 at 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 acurrate 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 -V2can be used to extract the QGP shear viscosity -For an acurrate 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 v2 is increased by 10%, one need to increase by in order to describe the same exp. data -10%uncertainties in V2 translate into 50% uncertainties for the extracted value of -V2can be used to extract the QGP shear viscosity -For an acurrate 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/CGC ; optical/fluctuations) -treatment of hadronic stage and freeze-out procedure: -EoS: EOS Q, EOS L, EOS L + chemical non-equil. HRG EOS -viscosities & relaxation times: -initialization for

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

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

  17. 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

  18. Effects of chemical composition of HRG on 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): change v2 by ~30%

  19. Effects of chemical composition of HRG on PCE vs.CE (HRG) Glauber Ideal hydro 30% 30% CGC P. Huovinen 07 Luzum &Romatschke 08 -PCE EoS vs. CE EoS (ideal hydro): change V2~30%influence ~100% -Constraining requires: a proper description of partial chemical equilibrium in HRG

  20. Effects of highly viscous hadronic stage on Ideal hydro 30-50% T. Hirano -highly viscous hadronic stage: change V2~30-50% influence ~100-150% -need viscous hydro + hadron cascade hybrid approach

  21. 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) -viscosities & relaxation times: -initialization for shear and bulk pressure

  22. 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 talk by P. Houvinen --more realistic EOS for hydro 0903 lattice data for QGP + PCE EOS for HRG

  23. 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) -viscosities & relaxation times: -initialization for shear and bulk pressure

  24. - 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

  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 Tcprevents 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 a critical slowing down , effects from bulk viscosity effects 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 : (PEC 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% recent progress: Heinz et al. 0907 -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. Luzum & Romatschke, PRC 2008 Glauber CGC Extracting from RHIC data --the current status of viscous hydrodynamics (uncertainties in ) -initial conditions: CGC vs. Glauber~100% recent progress: Heinz et al. 0907 -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: -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 - v2/ε:dependence on system size & shear viscosity -photon spectra -HBT radii … …

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

  36. System size dependence of shear viscous effects Song & Heinz PRC 08 -larger shear viscous suppression of elliptic flow in smaller systems -the slope of the multiplicity scaling ofv2/ε is sensitive to the value of shear viscosity

  37. System size dependence of shear viscous effects Song & Heinz PRC 08 -larger shear viscous suppression of elliptic flow in smaller systems -the slope of the multiplicity scaling ofv2/ε is sensitive to the value of shear viscosity

  38. System size dependence of shear viscous effects Song & Heinz PRC 08 -larger shear viscous suppression of elliptic flow in smaller systems -the slope of the multiplicity scaling ofv2/ε is sensitive to the value of shear viscosity

  39. Multiplicity scaling of v2/ε Song & Heinz PRC 08 -the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity -to reproduce the experimental data (slope), a constant is not enough!

  40. Multiplicity scaling of v2/ε Song & Heinz PRC 08 -the slope of the multiplicity scaling of v2/ε is sensitive to the value of shear viscosity -to reproduce the experimental data (slope), a constant is not enough! -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 - v2/ε:dependence on system size & shear viscosity -photon spectra -HBT radii … …

  42. EM probes: Photons Photon spectra Pion spectra K. Dusling, 0903 -Viscous hardening of PT-spectra is stronger for photons than hadrons -However, earlier thermalization also leads to harder photon spectra (Dusling 0903) -Photon spectra MAY HELP to constrain the 2-d range of QGP viscosity & thermalization time, together with other observables (V2 …)

  43. other observables that are sensitive to - v2/ε:dependence on system size & shear viscosity -photon spectra -HBT radii … …

  44. HBT radii S. Pratt QM09 without viscosity with viscosity - is sensitive to the QGP viscosity - However, viscosity is only one of the many ingredients that affect HBT radii (Pratt QM09) - HBT HELPS to constrain the QGP viscosity, together with other observables (V2 …)

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

  46. A short summary - is sensitive to A first attempt to constrain from RHIC data indicates 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 … … … …

  47. Thank You

  48. EOS EOS

  49. Qualitative effects of & on V2 ideal hydro Elliptical flow v2 Song & Heinz, 0909 viscous hydro (shear only) Change the flow profile during hydro evolution Flow + spectra correc. Spectra correc.: 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

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

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