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Perfect Fluid: flow measurements are described by ideal hydro

Phys. Rev. Lett. 97 162302 (2006). Measuring Viscosity at RHIC Sean Gavin Wayne State University Mohamed Abdel-Aziz Institut für Theoretische Physik, Frankfurt. Perfect Fluid: flow measurements are described by ideal hydro

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Perfect Fluid: flow measurements are described by ideal hydro

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  1. Phys. Rev. Lett. 97 162302 (2006) Measuring Viscosity at RHIC Sean Gavin Wayne State UniversityMohamed Abdel-Aziz Institut für Theoretische Physik, Frankfurt Perfect Fluid: flow measurements are described by ideal hydro Problem: all fluids have some viscosity -- can we measure it? I. Radial flow fluctuations: Dissipated by shear viscosity II. Contribution to transverse momentum correlations III. Implications of current fluctuation data

  2. Measuring Shear Viscosity Elliptic and radial flow suggest small shear viscosity • Teaney; Kolb & Heinz; Huovinen & Ruuskanen Problem: initial conditions & EOS unknown • CGC  more flow? larger viscosity? Hirano et al. Kraznitz et al.; Lappi & Venugopalan; Adil et al. Small viscosity or strong flow? Additional viscosity probes? What does shear viscosity do? It resists shear flow. flow vx(z) shear viscosity 

  3. Radial Flow Fluctuations small variations in radial flow in each event neighboring fluid elements flow past one another  viscous friction shear viscosity drives velocity toward the average damping of radial flow fluctuations  viscosity

  4. z Evolution of Fluctuations u momentum current for small fluctuations r u(z,t) ≈ vr  vr  shear stress momentum conservation diffusion equation for momentum current kinematic viscosity shear viscosity  entropy density s, temperature T

  5. Viscosity Broadens Rapidity Distribution viscous diffusion drives fluctuation gt   rapidity broadening random walk in rapidityyvs. proper time V = 2/0 V increase kinematic viscosity Ts formation at0 /0

  6. fluctuations diffuse through volume, drivingrg rg,eq Hydrodynamic Momentum Correlations momentum flux density correlation function rg rg r g,eqsatisfies diffusion equation Gardiner, Handbook of Stochastic Methods, (Springer, 2002) width in relative rapidity grows from initial value 

  7. How Much Viscosity? viscosity in collisions -- Hirano & Gyulassy supersymmetric Yang-Mills: s   pQCD and hadron gas: s~ 1 kinematic viscosity Abdel-Aziz & S.G effect on momentum diffusion: limiting cases: viscous liquid pQGP ~HRG~ 1 fm nearly perfect sQGP ~ (4 Tc)-1 ~ 0.1 fm wanted: rapidity dependence of momentum correlation function

  8. C()  Transverse Momentum Covariance observable: measures momentum-density correlation function C depends on rapidity interval  propose:measure C() to extract width 2 of rg

  9. Current Data? STAR measures rapidity width of pt fluctuations J.Phys. G32 (2006) L37 find width *increases in central collisions • most peripheral *~ 0.45 • central *~ 0.75 naively identify*with  freezeout  f,p~ 1 fm,  f,c~ 20 fm   ~ 0.09 fm at Tc~ 170 MeV  s~ 0.08 ~ 1/4

  10. Uncertainty Range we want: STAR measures: density correlation function may differ from rg maybe n  2* STAR, PRC 66, 044904 (2006) uncertainty range *   2*  0.08  s  0.3

  11. Current Data  Viscosity Hints!

  12. Measure pt Covariance for Clearer Picture

  13. Summary: small viscosity or strong flow? current fluctuation data compatible with compare to other observables with different uncertainties test the perfect liquid  viscosity info • viscosity broadens momentum correlations in rapidity • pt covariance measures these correlations

  14. sQGP + Hadronic Corona viscosity in collisions -- Hirano & Gyulassy supersymmetric Yang-Mills: s   pQCD and hadron gas: s~ 1 Broadening from viscosity Abdel-Aziz & S.G, in progress H&G  QGP + mixed phase + hadrons  T()

  15. Centrality Dependence centrality: mean parton path length STAR, J.Phys. G32 (2006) L37 freezeout time model Teaney, Lauret & Shuryak Abdel-Aziz & S.G, in progress rapidity width

  16. Covariance Momentum Flux covariance unrestricted sum: correlation function: C =0 in equilibrium 

  17. ptFluctuations Energy Independent STAR, Phys.Rev. C72 (2005) 044902 Au+Au, 5% most central collisions

  18. Flow Contribution dependence on maximumpt, max PHENIX flow added thermalization  2 = pt    pt  explained by blueshift? needed: more realistic hydro + flow fluctuations

  19. Covariance Momentum Flux want: STAR measures: where: two correlation functions:

  20. Thermalization + Flow M. Abdel-Aziz & S.G. blue-shift: • average increases • enhances equilibrium contribution flow added thermalization s1/2=200 GeV 130 GeV 20 GeV • blue-shift cancels in ratio participants

  21. Rapidity Dependence of Momentum Fluctuations momentum correlation function near midrapidity • relative rapidity yr = y1-y2 • weak dependence on ya = (y1+y2)/2 fluctuationsin rapidity window Abdel-Aziz, S.G take o~ 0.5, fo  2

  22. Uncertainty Range we want: STAR measures: density correlations momentum density correlations density correlation functionrn rn r n,eq may differ from rg maybe n  2* STAR, PRC 66, 044904 (2006) uncertainty range *   2*  0.08  s  0.3

  23. vanishes in equilibrium measures correlation function Transverse Momentum Covariance observable:

  24. Viscosity Broadens Rapidity Distribution viscous diffusion random walk in rapidityyvs. proper time V = 2/0 V kinematic viscosity Ts formation at0 /0

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