1. Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics Barbara Betz Disputationsvortrag Johann Wolfgang Goethe-Universität Frankfurt am Main 13/10/2009 Phys. Lett. B 675, 340 (2009), Prog. Part. Nucl. Phys. 62, 556 (2009), Phys. Rev. C 79, 034902 (2009), arXiv: 0907.2516 [nucl-th] (Nucl. Phys. A in press)

2. Barbara Betz Disputationsvortrag 213/10/2009 proton The QCD Phase Diagram initial state pre-equilibrium expanding fireball hadronization hadronic phase and freeze-out S. Bass, Talk Quark Matter 2001  Insights into theory of strong interactions (QCD)  Medium created in heavy- ion (HIC) collisions similar to the one created after Big Bang  Explore the phase diagram of QCD with HIC

3. Barbara Betz Disputationsvortrag 313/10/2009 „ dust “ The Expanding Medium From first principles, it is unclear if medium is … fluid  Data described by hydrodynamics  Small P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99,172301 (2007) Hydrodynamics: azimuthal anisotropy of emitted particles, parametrized by v 2 Medium behaves like an almost ideal fluid Particles interact, expansion determined by density gradient Particles don‘t interact, expansion independent of initial shape

4. Barbara Betz Disputationsvortrag 413/10/2009 Jet - Studies in HIC I Jet moving through dense matter, depositing its energy should eventually disappear Jet suppression: signal for creation of opaque matter (Quark-Gluon Plasma) STAR, Phys. Rev. Lett. 91 (2003) 072304 4 < p T trigger < 6 GeV/c p T assoc > 2 GeV/c Can energy lost by jets tell us something about medium properties? Trigger particle

5. Barbara Betz Disputationsvortrag 513/10/2009 PHENIX, Phys. Rev. C 77, 011901 (2008) Au+Au / p+p = 200 GeV Redistribution of energy to lower p T - particles Generation of Mach cone pattern Re-appearance of the away-side for low and intermediate p T assoc Mach cone angle sensitive to EoS: STAR, Nucl. Phys. A 774, 129 (2006) 4 < p T trigger < 6 GeV/c 0.15 < p T assoc < 4 GeV/c Reflect interaction of jet with medium Jet - Studies in HIC II

6. Barbara Betz Disputationsvortrag 613/10/2009 Hydrodynamics I Medium created in a HIC can be described using hydrodynamics Hydrodynamics represents (local) conservation of energy-momentum (local) charge For ideal hydrodynamics in local thermodynamical equilibrium Equation of State,,, For viscous hydrodynamics (Eckart frame),

7. Barbara Betz Disputationsvortrag 713/10/2009 Hydrodynamics II BB, D. Henkel and D. H. Rischke, Prog. Part.. Nucl. Phys. 62, 556 (2009) W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979) A. Muronga, Phys. Rev. C 76, 014909 (2007) BB, D. Henkel, and D. H. Rischke, Prog. Part. Nucl. Phys. 62, 556 (2009) Deriving the transport equations for viscous quantities up to 2nd order in gradients, starting from the Boltzmann equation

8. Barbara Betz Disputationsvortrag 813/10/2009 Modelling of Jets STAR, Phys. Rev. Lett. 95, 152301 (2005) residue of energy and momentum given by the jet Assumption of isochronous/isothermal freeze-out No interaction afterwards mainly flow driven  Conversion into particles Freeze-out: Jets can be modelled using (ideal) hydrodynamics:

9. Barbara Betz Disputationsvortrag 913/10/2009 Stopped Jet I Applying a static medium and an ideal Gas EoS for massless gluons Assume: Near-side jet is not modified by medium t=4.5/v fm BB et al., Phys. Rev. C 79, 034902 (2009) Bragg Peak Jet decelerates according to Bethe-Bloch formalism Mach cone Diffusion wake

10. Barbara Betz Disputationsvortrag 1013/10/2009 Stopped Jet II Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity Energy Flow Distribution Assuming: Particles in subvolume will be emitted into the same direction p T = 5 GeV BB et al., Phys. Rev. C 79, 034902 (2009) Strong influence of the Diffusion wake

11. Barbara Betz Disputationsvortrag 1113/10/2009 Modelling Jets using … Conclusion about Mach cones? pQCD AdS/CFT P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008) R. Neufeld et al, Phys. Rev. C 78, 041901 (2008) Strongly-coupled theory Pointing vector perturbation Momentum density perturbationEnergy density perturbation Weakly-coupled theory v=0.75 v=0.99955

12. Barbara Betz Disputationsvortrag 1213/10/2009 Heavy Quark Jets in pQCD vs AdS/CFT Compare weakly and strongly coupled models using heavy punch-through jet pQCD: Neufeld et al. source for a heavy quark AdS/CFT: Stress tables with R. Neufeld et al, Phys. Rev. C 78, 041901 (2008) p T = 3.14 GeV BB et al., Phys. Lett. B 675, 340 (2009) No Mach-like peaks: AdS/CFT: Strong influence of the Neck region Static medium and isochronous freeze-out needed for comparison t=4.5/v fm S. Gubser et al, Phys. Rev. Lett. 100, 012301 (2008) BB et al., Phys. Lett. B 675, 340 (2009) J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)

13. Barbara Betz Disputationsvortrag 1313/10/2009 L. Satarov et al, Phys. Lett. B 627, 64 (2005) Expanding Medium I Consider different jet paths b=0 Apply Glauber initial conditions and an ideal Gas EoS for massless gluons Focus on radial flow contribution Experimental results based on many events A. K. Chaudhuri, Phys. Rev. C 75, 057902 (2007), A. K. Chaudhuri, Phys. Rev. C 77, 027901 (2008) Two-particle correlation (T freeze-out < T crit = 130 MeV): represents near-side jet Jet 150 E tot = 5 GeV

14. Barbara Betz Disputationsvortrag 1413/10/2009 Expanding Medium II E tot = 5 GeV broad away-side peak double peaked structure due to non-central jets T trig p T trig = 3.5 GeV BB et al., Nucl. Phys. A in press (arXiv:0907.2516 [nucl-th]) PHENIX, Phys. Rev. C 77, 011901 (2008)

15. Barbara Betz Disputationsvortrag 1513/10/2009 Summary  Investigation of jet-medium interactions using (3+1)d ideal hydrodynamics for different energy and momentum loss scenarios (schematic source term, pQCD, AdS/CFT)  Diffusion wake is always created if dM/dx > threshold  Different impacts of pQCD and AdS/CFT source terms  Experimentally observed signal can be obtained from different contributions of several jets in an expanding medium Deflection of Mach cones Structure unrelated to EoS Single jet events  Transport equations for dissipative hydrodynamics to 2nd order in gradients Fundamental for any numerical application of viscous effects

16. Barbara Betz Disputationsvortrag 1613/10/2009 Backup

17. Barbara Betz Disputationsvortrag 1713/10/2009 t=4.5/v fm v=0.999 Punch – Through Jet I Applying a static medium and an ideal Gas EoS for massless gluons Maximal fluid response BB et al., Phys. Rev. C 79, 034902 (2009) Assume: Near-side jet is not modified by medium

18. Barbara Betz Disputationsvortrag 1813/10/2009 Punch – Through Jet II Diffusion wake causes peak in jet direction Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity Energy Flow Distribution Assuming: Particles in subvolume will be emitted into the same direction p T = 5 GeV BB et al., Phys. Rev. C 79, 034902 (2009)

19. Barbara Betz Disputationsvortrag 1913/10/2009 Creation of Bow Shock for smaller v strengthens peak in jet direction Does the jet-pattern reproduce the features of a Mach cone? Velocity dependence of the emission angle p T = 5 GeV Punch – Through Jet III BB et al., Phys. Rev. C 79, 034902 (2009)

20. Barbara Betz Disputationsvortrag 2013/10/2009 Still influence of diffusion wake Transverse momentum deposition: from explosion of matter t=4.5/v fm Vorticity conservation Punch – Through Jet IV BB et al., Phys. Rev. C 79, 034902 (2009)

21. Barbara Betz Disputationsvortrag 2113/10/2009 Punch – Through vs Stopped Jet Similar freeze-out patterns p T = 5 GeV BB et al., Phys. Rev. C 79, 034902 (2009) p T = 5 GeV Punch-Through JetStopped Jet

22. Barbara Betz Disputationsvortrag 2213/10/2009 Punch – Through Jet: Velocity Scan t=4.5/v fm

23. Barbara Betz Disputationsvortrag 2313/10/2009 Near-side Jet t=4.5/v fm Assuming energy-momentum conversation and the disapparance of the near-side jet after t=0.5fm Reduction of diffusion wake Not strong enough to be seen in the freeze-out pattern

24. Barbara Betz Disputationsvortrag 2413/10/2009 The Diffusion Wake G. Burau, Genua Harbour, September 2008 The diffusion wake exists!

25. Barbara Betz Disputationsvortrag 2513/10/2009 Why linearized Hydro is not so good Head wave pile-up - Non-linear hydrodynamics - Signal not well understood - Non-Mach cone angle Source - Non-linear hydrodynamics - Non-thermalized Diffusion Wake - Proportional to source - Not seen experimentally Mach Cone -Linear hydrodynamics -Connected to EoS

26. Barbara Betz Disputationsvortrag 2613/10/2009 Momentum Deposition BB et al., J. Phys. G 35, 104106 (2008) dE/dx = 1.4 GeV/fm Static medium for different energy and momentum loss rates: Cooper-Frye freeze-out after t=7.2fm Double-peaked structure visible for (dM/dx)/(dE/dx) 12.8%

27. Barbara Betz Disputationsvortrag 2713/10/2009 Stopped Jet Jet stops after t=4.5/v fm Vorticity conservation t FO =4.5/v fmt FO =6.5/v fmt FO =8.5/v fm Diffusion wake still present BB et al., Phys. Rev. C 79, 034902 (2009)

28. Barbara Betz Disputationsvortrag 2813/10/2009 Stopped Jet t FO =4.5/v fmt FO =6.5/v fmt FO =8.5/v fm Diffusion wake causes peak in jet direction Larger impact of thermal smearing BB et al., Phys. Rev. C 79, 034902 (2009)

29. Barbara Betz Disputationsvortrag 2913/10/2009 Different Contributions E Mach 53.9%P x Mach 6.5% E Diff -12.3%P x Diff 18.7% E Neck 57.4%P x Neck 73.7% E Head 1.0%P x Head 1.0% t=4.5/v fm BB et al., Phys. Rev. C 79, 034902 (2009) p T =2. 5 GeV

30. Barbara Betz Disputationsvortrag 3013/10/2009 Energy-Momentum Relation general:

31. Barbara Betz Disputationsvortrag 3113/10/2009 Jet – Energy Loss Studies Jet deposits energy and momentum along a trajectory Applying linearized hydrodynamics Mach cone for sound waves Diffusion wake J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)

32. Barbara Betz Disputationsvortrag 3213/10/2009 Jets in AdS/CFT I Heavy Quark String N=4 SYM Thermal Background Black hole in AdS space R. Fries et al, Phys. Rev. D 75, 106003 (2007) Analogues: Mach cone in coordinate space S. Gubser et al., Phys. Rev. Lett. 100, 012301 (2008)

33. Barbara Betz Disputationsvortrag 3313/10/2009 Jets in AdS/CFT II Pattern similar to pQCD P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008) Jet travelling at v=0.75 Poynting vector perturbationEnergy density perturbation Diffusion Wake contribution Attention: No clear Mach cone signal

34. Barbara Betz Disputationsvortrag 3413/10/2009 Non-Mach correlations caused by Neck region Jets in AdS/CFT III J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)

35. Barbara Betz Disputationsvortrag 3513/10/2009 Jets in pQCD I Mach cone in coordinate space R. Neufeld et al, Phys. Rev. C 78, 041901 (2008) Considering a static medium and linearized hydrodynamics for a punch-though jet Mach cone signal & Diffusion Wake

36. Barbara Betz Disputationsvortrag 3613/10/2009 Jets in pQCD II Mach cone in coordinate space Contour plots of magnitude of perturbed momentum density Strong flow in jet-direction R. Neufeld et al., Phys. Rev. C 79, 054909 (2009)

37. Barbara Betz Disputationsvortrag 3713/10/2009 pQCD Source Term I Idea: External color field generated by fast parton propagating through QGP with Since Lorentz forced considered to lowest order in coupling g

38. Barbara Betz Disputationsvortrag 3813/10/2009 pQCD Source Term II For a parton moving with v=const. and omitting dielectric screening: with

39. Barbara Betz Disputationsvortrag 3913/10/2009 pQCD Source Term III For ultraviolett and infrared cut-off: E p energy of fast parton

40. Barbara Betz Disputationsvortrag 4013/10/2009 J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009) The Neck Zone in pQCD vs AdS/CFT Strong transverse flow No strong transverse flow pQCDAdS/CFT BB et al., Phys. Lett. B 675, 340 (2009)

41. Barbara Betz Disputationsvortrag 4113/10/2009 Heavy Quark Jets in pQCD vs AdS/CFT I Idea: Compare weakly and strongly coupled models Using heavy quark punch-through jet pQCD: Neufeld et al. source for a heavy quark AdS/CFT: Stress tables provided by S. Gubser, A. Yarom and S. Pufu with Applying ideal hydrodynamics for a static medium and an ideal gas EoS of massless gluons Assume that the near-side jet is not modified by the medium BB et al., Phys. Lett. B 675, 340 (2009) t=4.5/v fm Neufeld et al, Phys. Rev. C 78, 041901 (2008)

42. Barbara Betz Disputationsvortrag 4213/10/2009 No Mach-like peaks: Isochronous freezeout needed to compare pQCD and AdS/CFT Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity p T = 3.14 GeV Strong influence of the Neck region J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009) BB et al., Phys. Lett. B 675, 340 (2009) Heavy Quark Jets in pQCD vs AdS/CFT II

43. Barbara Betz Disputationsvortrag 4313/10/2009 Mach-like peaks & Momentum Flow Distribution Independent of p T - cut Strong impact of diffusion wake Assuming: Particles in subvolume will be emitted into the same direction BB et al., Phys. Lett. B 675, 340 (2009) Heavy Quark Jets in pQCD vs AdS/CFT III

44. Barbara Betz Disputationsvortrag 4413/10/2009 Expanding Medium Jet 90Jet 120 Jet 150 Jet 180

45. Barbara Betz Disputationsvortrag 4513/10/2009 Expanding Medium Jet 150Jet 180 Jet 120

46. Barbara Betz Disputationsvortrag 4613/10/2009 Expanding Medium E tot = 5 GeV broad away-side peak double peaked structure T trig p T trig = 3.5 GeV PHENIX, Phys. Rev. C 77, 011901 (2008)

47. Barbara Betz Disputationsvortrag 4713/10/2009 Expanding Medium E tot = 10 GeV Strong impact of the Diffusion wake broad away-side peak double peaked structure due to non-central jets Causes smaller dip for p T =2 GeV PHENIX, Phys. Rev. C 77, 011901 (2008) T trig p T trig = 7.5 GeV

48. Barbara Betz Disputationsvortrag 4813/10/2009 Expanding Medium E tot = 5 GeV broad away-side peak Pure energy depositionNo conical distribution in expanding medium Jet 180: No peaks on away-side T trig p T trig = 3.5 GeV

49. Barbara Betz Disputationsvortrag 4913/10/2009 Expanding Medium en. and mom. loss pure energy loss E tot = 10 GeV T trig p T trig = 7.5 GeV E tot = 5 GeV T trig p T trig = 3.5 GeV E tot = 5 GeV T trig p T trig = 3.5 GeV

50. Barbara Betz Disputationsvortrag 5013/10/2009 Expanding Medium E tot = 4.3 GeV broad away-side peak T trig p T trig = 3.0 GeV

51. Barbara Betz Disputationsvortrag 5113/10/2009 Expanding Medium Jet deposition stopped E tot = 5 or 10 GeV T trig p T trig = 3.5 and 7.5 GeV

52. Barbara Betz Disputationsvortrag 5213/10/2009 Expanding Medium For b=6 fm Distortion of the conical structure Dependence on background flow (centrality)

53. Barbara Betz Disputationsvortrag 5313/10/2009 Cooper-Frye Freeze-out: The Caveat: Freeze-out Prescription Assumption of isochronous/isothermal freeze-out No interaction afterwards mainly flow driven http://www.rnc.blb.gov/ssalur/www/Research3.html

54. Barbara Betz Disputationsvortrag 5413/10/2009 Isothermal and isochronous freeze-out lead to very similar results Isothermal Freeze-out Beak occurs for non-central jetsJet 150 Jet 180

55. Barbara Betz Disputationsvortrag 5513/10/2009 Backup (General)

56. Barbara Betz Disputationsvortrag 5613/10/2009 Jet - Studies in HIC  Assumption : Correlations from flow anisotropy and jets are uncorrelated ZYAM (Zero Yield At Minimum)  Subtraction of: estimated elliptic flow modulated background  can leads to: double peaked structure Background: Particle correlation from elliptic flow J. Ulery [STAR], PoS LHC07, 036 (2007) Two-source model:

57. Barbara Betz Disputationsvortrag 5713/10/2009 Jet - Studies in HIC p T -dependence (associated jet): double peaked structure seems to get broader (but within errorbars) p T -dependence (trigger jet): one peak structure evolves (possible punch-through) PHENIX, Phys. Rev. C 77, 011901 (2008)

58. Barbara Betz Disputationsvortrag 5813/10/2009 Jet - Studies in HIC J. Putschke, Talk at RHIC and AGS Users Meeting 2009

59. Barbara Betz Disputationsvortrag 5913/10/2009 Jet - Studies in HIC Centrality dependence: double peaked structure for central collisions one peak structure for very peripheral collisions PHENIX, Phys. Rev. Lett. 97, 052301 (2006)

60. Barbara Betz Disputationsvortrag 6013/10/2009 Jet - Studies in HIC Investigation of path length dependence: Double-peaked structure becomes more pronounced out-of-plane A. Sickeles [PHENIX], Eur. Phys. J. C 61, 583 (2009)

61. Barbara Betz Disputationsvortrag 6113/10/2009 Jet - Studies in HIC W. G. Holzmann [PHENIX], arXiv:0907.4833 [nucl-ex] Geometry dependence, path length dependence 18 bins with 5 deg

62. Barbara Betz Disputationsvortrag 6213/10/2009 Experimental data show superposition of Mach cone structure and deflected jets J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007) Deflected jetMach Cone Jet - Studies in HIC Is the double-peaked structure due to a Mach cone formation? p trig T =3 – 4 GeV, p assoc T =1 – 2 GeV

63. Barbara Betz Disputationsvortrag 6313/10/2009 Jet - Studies in HIC N. N. Ajitanand [PHENIX], Nucl. Phys. A 783, 519 (2007) Three-particle correlation shows superposition of Mach cone structure and deflected jets Simulation for deflected jets and Mach cone High-p T trigger Same-Side Jet

64. Barbara Betz Disputationsvortrag 6413/10/2009 Jet - Studies in HIC Projection along  =const. shows away-side peak N. N. Ajitanand [PHENIX], Poster Quark Matter 2009

65. Barbara Betz Disputationsvortrag 6513/10/2009 Heavy Quarks B. Biritz [STAR], arXiv:0907.3937[nucl-ex] 3.0 < p t trig < 6.0 GeV 0.15 < p t trig < 0.5 GeV Au+Au 200 GeVCu+Cu 200 GeV Non-photonic e-h correlations to probe heavy quark jet-medium interactions

66. Barbara Betz Disputationsvortrag 6613/10/2009 Jet - Studies at SPS Energies CERES, Phys. Lett. B 687, 259 (2009) Pb+Pb 158AGeV 2.5 < p t trig < 4.0 GeV 1.0 < p t assoc < 2.5 GeV

67. Barbara Betz Disputationsvortrag 6713/10/2009 Jet - Studies at SPS Energies CERES, Phys. Lett. B 687, 259 (2009) Asymmetry: Hard scattering at SPS dominated by large-x partons Positive trigger: R -+ close to medium value energy deposition

68. Barbara Betz Disputationsvortrag 6813/10/2009 Jet - Studies at SPS Energies S. Kniege, PhD Thesis, Frankfurt (2009) No sensitivity for three-particle correlations

69. Barbara Betz Disputationsvortrag 6913/10/2009 Jet - Studies Energy Scan J. Jia, Eur. Phys. J. C 62, 255 (2009) p trig T =2.5 – 4 GeV, p assoc T =1 – 2.5 GeV  (PHENIX)=0.7,  (CERES)=0.5 Trigger yield at SPS: stronger trigger bias, more non-trigger jets

70. Barbara Betz Disputationsvortrag 7013/10/2009 High p T -correlations Effect of global momentum conservation? Medium response??? Peaked away-side structure modelled by UrQMD Pb+Pb (0-5%) 158AGeV C. Blume, PoS(Confinement8) 110, 2008

71. Barbara Betz Disputationsvortrag 7113/10/2009 Full Jet Reconstruction I J. Putschke, Talk at RHIC and AGS Users Meeting 2009 Full jet reconstruction questions ZYAM

72. Barbara Betz Disputationsvortrag 7213/10/2009 Full Jet Reconstruction II No apparent v 2 modulation in jet-hadron vs. di-hadron correlations J. Putschke, Talk at RHIC and AGS Users Meeting 2009

73. Barbara Betz Disputationsvortrag 7313/10/2009 Full Jet Reconstruction III Jet-hadron away-side significantly narrower J. Putschke, Talk at RHIC and AGS Users Meeting 2009

74. Barbara Betz Disputationsvortrag 7413/10/2009 Mach Cone Deformation L. Satarov et al, Phys. Lett. B 627, 64 (2005) Change in Mach angle due to background flow

75. Barbara Betz Disputationsvortrag 7513/10/2009 Shock waves in A 1 +A 2 Collisions H. G. Baumgardt et al., Z. Physik A 273 (1975) 359 Sketch of a light nucleus penetrating through a heavier one:

76. Barbara Betz Disputationsvortrag 7613/10/2009 Shock waves in A 1 +A 2 Collisions H. G. Baumgardt et al., Z. Physik A 273 (1975) 359 Sketch of a non-central collision of a light nucleus with a heavier one

77. Barbara Betz Disputationsvortrag 7713/10/2009 Shock waves in Ne+U Collisions I P. Rau et al., to be published (free streaming)or

78. Barbara Betz Disputationsvortrag 7813/10/2009 Shock waves in Ne+U Collisions II (free streaming)or P. Rau et al., to be published

79. Barbara Betz Disputationsvortrag 7913/10/2009 Boosted Thermal Distribution Isotropically distributed thermal momentum (local rest frame) gets peaked at small angles in the laboratory frame P. Rau, private communication

80. Barbara Betz Disputationsvortrag 8013/10/2009 Smoke Rings BB et al, Phys. Rev. C 76, 044901 (2007) Vorticity generated by a jet, t=11.52 fm, static medium

81. Barbara Betz Disputationsvortrag 8113/10/2009 Mach Cones in Transport Theory D. Molnar, arXiv:0908.0299 [nucl-th] local energy density “ perturbative ” scenario momentum density “ pure energy ” scenario Diffusion wake

82. Barbara Betz Disputationsvortrag 8213/10/2009 Energy Loss Stopping power for muons in copper PDG, J. Phys. G 33, 1 (2006)

83. Barbara Betz Disputationsvortrag 8313/10/2009 The Ridge Ridge: Long-ranged structure in  PHYTHIA simulation for p+p0-30% Au+Au PHOBOS, J. Phys. G 35, 104080 (2008)

84. Barbara Betz Disputationsvortrag 8413/10/2009 Geometry of HIC

85. Barbara Betz Disputationsvortrag 8513/10/2009 Mach Cone – Speed of Sound Emission Angle of the Mach cone ~ Assuming v jet ~ 1 ~ 0.57  = 1.0 rad massless QGP: c s ~ 0.57  = 1.0 rad ~ 0.3  = 1.3 rad Hadronic matter: c s ~ 0.3  = 1.3 rad ~ 0  = 1.5 rad 1 st order p.t.: c s ~ 0  = 1.5 rad F. Wang, Talk Quark Matter 2006

86. Barbara Betz Disputationsvortrag 8613/10/2009 Elliptic Flow and Viscosity I M. Luzum and P. Romatschke, Phys. Rev. C 78:034915 (2008) Initial conditions matter

87. Barbara Betz Disputationsvortrag 8713/10/2009 Z. Xu and C. Greiner, Phys. Rev. C 79:014904 (2009) Initial conditions matter Elliptic Flow and Viscosity II

88. Barbara Betz Disputationsvortrag 8813/10/2009 Viscous Hydrodynamics W. Israel, J.M. Stewart, Ann. Phys. 118, 341 (1979) A. Muronga, Phys. Rev. C 76, 014909 BB, D. Henkel, and D. H. Rischke, Prog. Part. Nucl. Phys. 62, 556 (2009) BB, H. Niemi, and D. H. Rischke, in preparation Deriving the transport equations for starting from the Boltzmann equation

89. Barbara Betz Disputationsvortrag 8913/10/2009 Other Jet-Medium Models I Lattice QCD EoS T. Renk and J. Ruppert, Phys. Rev. C 73, 034907 (2006) Determines angular correlation pattern Fireball model BDMPS-like energy loss f: „fraction … of energy lost to the medium [that] excites a collective mode“ (1-f): „remaining energy fraction … [that] in essence heats the medium and leads to some amount of the collective drift along the jet axis…“ sound wave diffusion Mach cones only if dM/dx << dE/dx

90. Barbara Betz Disputationsvortrag 9013/10/2009 Other Jet-Medium Models II A. Chaudhuri and U. Heinz, Phys. Rev. Lett. 97, 062301 (2006) First-order phase transition Calculates the azimuthal distribution Expanding (2+1)d hydro (AZHYDRO) Source term: Quenched jet Diffusion wake Isothermal Freeze-out

91. Barbara Betz Disputationsvortrag 9113/10/2009 Other Jet-Medium Models II Hottest region at the head of the jet Effect from diffusion wake No Mach cone-like correlation if dE/dx = dM/dx A. Chaudhuri and U. Heinz, Phys. Rev. Lett. 97, 062301 (2006)

92. Barbara Betz Disputationsvortrag 9213/10/2009 Other Jet-Medium Models III A. Chaudhuri, Phys. Rev. C 75, 057902 (2007) AZHYDRO, for different jet paths: Azimuthal distri- bution of pions for different jet paths Normalized, azimuthal distribution of pions, averaged over different jet trajectories for b=3fm Au+Au collisions

93. Barbara Betz Disputationsvortrag 9313/10/2009 Other Jet-Medium Models III A. Chaudhuri, Phys. Rev. C 77, 027901 (2008)  jet may vary: Implicit assumption: punch-through jets Normalized, jet path averaged azimuthal distribution of pions for b=2.3fm, 4.1fm, 12.1fm Au+Au collisions STAR: 0.15 p assoc T 4.0 GeV 4.0 p trig T 6.0 GeV PHENIX: 2.5 p assoc T 4.0 GeV 1.0 p trig T 2.5 GeV

94. Barbara Betz Disputationsvortrag 9413/10/2009 Energy-Momentum Relation On-shellness: Heisenbergs uncertainty relation: Large number of collisions small large