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Elliptic flow and shear viscosity in a parton cascade approach

Elliptic flow and shear viscosity in a parton cascade approach. G. Ferini INFN-LNS, Catania. P. Castorina, M. Colonna, M. Di Toro, V. Greco. Outline. Momentum anisotropy as a measure of plasma properties Reminder of v 2 & v 4  First results at RHIC

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Elliptic flow and shear viscosity in a parton cascade approach

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  1. Elliptic flow and shear viscosity in a parton cascade approach G. Ferini INFN-LNS, Catania P. Castorina, M. Colonna, M. Di Toro, V. Greco

  2. Outline Momentum anisotropy as a measure of plasma properties • Reminder of v2 & v4 First results at RHIC • Transport approach to study finite /s effects • v2 scaling with eccentricity and system size  dependence on /s  effects of freeze-out • v2(pT) & v4(pT)  1/4 < /s< 1/2 • Conclusions

  3. A measure of the Interaction: Elliptic Flow z y x py px 0 Free streaming v2=0 c2s=dP/de Perform a Fourier expansion of the momentum space particle distributions CASCADE =10 mb Similar trend in hydro Good probe of early pressure • v2 is the 2nd harmonic Fourier coeff. • of the distribution of particles. The analysis can be extended !

  4. If Elliptic Flow is very large To balance the minimum a v4 > (10v2-1)/34 is required v4 > 4.4% if v2=25% STAR, J. Phys. G34 (2007) v2 and v4 contain rich information on /s

  5. First stage of RHIC Parton cascade Hydrodynamics Parton elastic 22 interactions (finite mean free path) No microscopic details (mean free path  -> 0) • Good description of hadron spectra and v2(pT) • Mass ordering of v2 versus pT + EoS v2 saturation pattern reproduced D. Molnar & M. Gyulassy, NPA 697 (02)

  6. It’s not that perfect … • Is it really zero shear viscosity ? Not too peripheral But finite mean free path calls for a transport approach! B. I. Abelev et al., (STAR) Nucl-ex 0801.3466 Not too high pT Not too high harmonics STAR, J. Phys. G34 (2007)

  7. e & v2 B. I. Abelev et al., (STAR) Nucl-ex 0801.3466 Bhalerao et al., PLB627(2005) Hydrodynamics 2v2/e time Ideal Hydrodynamics: Indipendent of - impact parameter - system size Data show evidence for deviation from hydro scaling v2/ This calls for a transport approach!

  8. Transport approach Solved discretizing the space in (h, x, y)a cells Collision integral not solved with the geometrical interpretation, but with a localstochastic sampling Collisions in a box Several checks in ultra- relativistic conditions m=0 The approach provides a good framework for multiparticle collisions Z. Xhu, C. Greiner, PRC71(04)

  9. Shear Viscosity Small viscosity Large cross sections Strong couplings  beyond pQCD R. Lacey et al., PRL99(2006) 1)Hydrodynamics means h=0 2)Quantum mechanism h/s > 1/15 : 3) 4 SYM + Gauge theory g ->∞: Can we constrain /s with vn? Smaller than any other known fluid!

  10. v2/e and the Shear Viscosity We can simulate a constant shear viscosity during the HIC Cascade code Relativistic Kinetic theory =cell index in the r-space We have used pQCD-like cross section with screening mass Hydrodynamics The viscosity is kept constant varying as In agreement with data v2/e is not constant -> finite viscosity Au+Au @200 AGeV

  11. Elliptic flow sensitive to the Shear Viscosity Sensitivity increasing at larger pT Intermediate pT can say more about /s Au+Au @ 200 AGeV b=9 fm b=7 fm b=5 fm b=3 fm

  12. Going to higher momentum anisotropies … v4 Finite minimal viscosity is consistent also with the v4 v4 more sensitive to the viscosity DATA b=9 fm

  13. v2 and v4 sensitivity to /s

  14. v2/ and v2/<v2> as a function of pT /s=1/2 /s=1/ Au+Au @ 200 AGeV Au+Au @ 200 AGeV v2/(pT) sensitive to /s Larger violation of the scaling at higher viscosity Reduced sensitivity to /s Similar results for Cu+Cu • Scaling for both v2/<v2> and v2/ • Agreement with PHENIX data for v2/<v2> /s1/4 closer to data

  15. Of course it is more complex… PHENIX PRL (2007) STAR (arXiv 2008)  v2/ does not scale! v2/<v2> scales! Can a cascade approach account for this? Freeze-out is crucial!

  16. Elliptic flow sensitive to freeze out For <c=0.7 GeV/fm3 collisions are switched off /s=1/4 b=5 fm  PHENIX /s=1/4 Au+Au @ 200 AGeV b=3 fm Coalescence plays a role Sensitivity increasing with b Indeed at that pT QNS is observed! V2(pT) of partons not directly comparable with data

  17. v2/ and v2/<v2> with freeze-out /s=1/4 No freeze-out No freeze-out v2/ scaling broken v2/<v2> scaling kept! (about 40% in b=3-9 fm) Cascade can get both features: • V2/broken in a way similar to STAR data • Agreement with STAR measurements of v2/<v2>

  18. v2(pT) as a measure of /s v2/<v2> scaling reproduced, what about v2 absolute value?  PHENIX /s=1/4 /s=1/2 /s=1/ • /s<1/2  too low v2(pT) at pT1.5 GeV/c • comparison with baryon and meson v2(pT) can constrain /s better (need for coalescence) • v4…. (work in progress)

  19. Conclusions • Summary • v2/<v2> () scaling holds at finite /s • v2/ breaking of the scaling • v2/<v2> scaling • v2(pT) hints at 1/4</s<1/2  (+ coalescence!?) • v4(pT) appears more sensitive to /s (work in progress) reproduced by a cascade approach (+ freeze-out) • Future Developments • Dynamical implementation of Greco-Ko-Levai coalescence model • what does go on for LHC conditions?

  20. First estimate of Shear Viscosity The v2/e scaling point to a viscosity of about 1/4p i.e. around the bound limit DATA Au+Au @ 200 A GeV Larger violation of the scaling at lower viscosity -> study of Cu+Cu Au+Au @ 200 A GeV

  21. Averaged elliptic flow Romatschke Greiner

  22. V2(pT) in viscous hydrodynamics How sensitive is elliptic flow to finite /s? P. Romatschke H. Song & U. Heinz

  23. Scaling of time evolution with the system size Hydrodynamics Cascade Au+Au @ 200 AGeV As in hydro in the early evolution v2/ scales with system size At the end a significant breaking is observed

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