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Momentum Anisotropies -- Probing the detailed Dynamics

Momentum Anisotropies -- Probing the detailed Dynamics. Peter F. Kolb. Department of Physics and Astronomy State University of New York Stony Brook, NY 11794 with support from the Alexander von Humboldt Foundation. Brookhaven National Laboratory Flow and QGP Workshop November 18, 2003.

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Momentum Anisotropies -- Probing the detailed Dynamics

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  1. Momentum Anisotropies --Probing the detailed Dynamics Peter F. Kolb Department of Physics and Astronomy State University of New York Stony Brook, NY 11794 with support from the Alexander von Humboldt Foundation Brookhaven National LaboratoryFlow and QGP Workshop November 18, 2003 Momentum Anisotropies

  2. With the given symmetries and the chosen coordinate system: no sin terms for equal nuclei and z = 0 no odd cos terms Non-Central Collisions Feature Broken Symmetry Characterize azimuthal dependence of the resulting observables by their Fourier expansion Momentum Anisotropies

  3. PFK and U. Heinz, nucl-ex/0204061 Teaney, Lauret, Shuryak, nucl-th/0110037 * … at very early stages Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (2001) 58 PFK, J. Sollfrank and U.Heinz, PRC 62 (2000) 054909 * requires strong rescattering Z.W. Lin and C.M. Ko, PRC 65 (2002) 034904 * is sensitive on the nuclear equation of state Greco, Levai, Ko, Molnar, Voloshin, Fries, Nonaka, Bass, Müller, Sorensen D. Molnar and M. Gyulassy, NPA 698 (2002) 379 PFK et al., PLB 500 (2001) 232 * shows a strong hydrodynamic mass effect * shows a quark counting rule Elliptic Flow - A Prominent Observable reaching the hydrodynamic limit on a timescale < 1 fm/c indicating a soft transition region common partonic flow heavier particles pick up larger <pT> in the common flow field Momentum Anisotropies

  4. PHENIX Collaboration, nucl-ex/0305013 Elliptic Flow at Large Pt is HUGE ! PHENIX Collaboration, nucl-ex/0305013 v2 = 0.25 means that there are 3 times as many particles emitted into the reaction plane than out of the reaction plane!Furthermore the distribution is not elliptic any longer! Momentum Anisotropies

  5. PFK, Phys. Rev. C 68 (2003) 031902(R) Higher order term to Counteract ? develops a minimum in cartesian coordinates at x=0 for v2 > 0.1 To balance the minimum a v4 > (10v2-1)/34 is required (this brings the second derivative of y(x) at x=0 to vanish). Momentum Anisotropies

  6. PFK, Phys. Rev. C 68 (2003) 031902(R) A quadrupole modulation of several percent can be expected ! Differential Expectations on Higher v’s From a recent hydrodynamic calculation to describe collisions at 200 GeV PFK, and R. Rapp, PRC 67 (2003) 044903 It is however not sufficient to balance the peanut shape Momentum Anisotropies

  7. coordinate space quantify anisotropies Geometric Anisotropy is Rapidly Converted to Momentum Space Momentum Anisotropies

  8. A short Digression on Fourier Coefficients Distribution within the reaction plane Distribution out of the reaction plane for a delta-function like distribution Momentum Anisotropies

  9. coordinate space momentum space quantify anisotropies Geometric Anisotropy is Rapdily Converted to Momentum Space Momentum Anisotropies

  10. Elliptic Flow in the Blast Wave Blast wave parametrization for non-central collisions Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (01) 58 Radial rapidity-field with angular modulation: Freeze-out on azimuthally symmetric hypersurface of temperature T: Collapse of the radial integration onto shell: Momentum Anisotropies

  11. Elliptic Flow in the Blast Wave Reproduces momentum - and mass dependenceof elliptic anisotropy Tdec = 140 MeV r0= 0.58 f2= 7.7 % Momentum Anisotropies

  12. Anisotropic Flow in the Blast Wave Blast wave parametrization for non-central collisions Huovinen, PFK, Heinz, Ruuskanen, Voloshin, PLB 503 (01) 58 Radial rapidity-field with angular modulation: Freeze-out on azimuthally symmetric hypersurface of temperature T: Collapse of the radial integration onto shell: Momentum Anisotropies

  13. negative f4 positive f4 1 % distortion 2 % distortion Blast Wave - Influence of f4 Momentum Anisotropies

  14. negative f6 positive f6 1 % distortion 2 % distortion Blast Wave - Influence of f6 Momentum Anisotropies

  15. expand for small anisotropies Sensitivity on f2 and f4 at some fixed transverse momentum (here pT =2 GeV) … an additional small quadropoledistortion in the flow field yieldsa large quadrupole moment inthe particle distribution A purely elliptic flow anisotropyproduces a small quadrupolemoment after folding with the thermal distribution… Momentum Anisotropies

  16. PFK, Phys. Rev. C 68 (2003) 031902(R) Parameterize surface in the transverse plane, i.e. for for even n with normal vector Cooper Frye freeze-out from the lense with weights on the emission angle Anisotropies from a Black Lense Carry the idea of Shuryak and Voloshin to higher levels (higher orders): PRC 66 (2002) 027902 NPA 715 (2003) 379 pure surface emission in the high pT limit (i.e. from extreme jet-quenching) Momentum Anisotropies

  17. Limiting Anisotropies versus Centrality PFK, Phys. Rev. C 68 (2003) 031902(R) Extremely interesting centrality dependence This picture predicts a peanut like distribution as well! Momentum Anisotropies

  18. 2 for mesons3 for baryons quarks mesons baryons 1/4 1/3 One Thought on Coalescence assume there are no higher order anisotropies on the quark level See talk by Art Poskanzer for experimental results! Momentum Anisotropies

  19. Ideally, triple differentially for different centrality classes: with odd coefficients at Anisotropies are generated early in the evolution probe the hottest stages very sensitve on details of the flow fields and dynamics will allow very quantitative statementsfrom all model calculations Summary: Why Study Higher Harmonics ? Get a full picture of the transverse momentum spectrum Momentum Anisotropies

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