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Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics

Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics. Barbara Betz Thanks goes to: Miklos Gyulassy, Igor Mishustin, Jorge Noronha, Dirk Rischke, Philip Rau, Horst Stöcker, and Giorgio Torrieri. Phys. Lett. B 675 , 340 (2009), Phys. Rev. C 79 , 034902 (2009),

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Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics

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  1. Jet Propagationand Mach-Cone Formationin (3+1)-dimensional IdealHydrodynamics Barbara Betz Thanks goes to: Miklos Gyulassy, Igor Mishustin, Jorge Noronha, Dirk Rischke, Philip Rau, Horst Stöcker, and Giorgio Torrieri Phys. Lett. B 675, 340 (2009), Phys. Rev. C 79, 034902 (2009), arXiv: 0907.2516 [nucl-th]

  2. 4 < pTtrigger < 6 GeV/c • pTassoc > 2 GeV/c STAR, Phys. Rev. Lett. 91 (2003) 072304 Explore The Matter Created in HIC • Data described by hydrodynamics P. Romatschke et al., Phys. Rev. Lett. 99,172301 (2007) • Jets are suppressed • System is dense and opaque • Fluid behaviour • Can energy lost by jets tell us something about medium properties?

  3. 4 < pTtrigger < 6 GeV/c • 0.15 < pTassoc < 4 GeV/c Au+Au / p+p = 200 GeV STAR, Nucl. Phys. A 774, 129 (2006) PHENIX, Phys. Rev. C 77, 011901 (2008) Jet - Studies in HIC I • Redistribution of energy to lower pT-particlesGeneration of Mach cone pattern • Re-appearance of the away-side for low and intermediate pTassoc • Mach cone angle sensitive to EoS: • Reflect interaction of jet with medium

  4. Jet - Studies in HIC II • Is the double-peaked structure due to a Mach cone formation? • ptrigT=3 – 4 GeV, passocT=1 – 2 GeV • Deflected jet • Mach Cone J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007) • Experimental data show • superposition of Mach cone • structure and deflected jets

  5. The Theory Part

  6. Ideal Hydrodynamics • 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

  7. STAR PRL 95 (2005) 152301 Modelling of Jets • Jet deposition mechanism unclear • Jets can be modelled using hydrodynamics: • not the source term of the jet • residue of energy and momentum given by the jet

  8. The Caveat: Freeze-out Prescription • Cooper-Frye Freeze-out: • mainly flow driven • Assumption of • isochronous/isothermal freeze-out • No interaction afterwards http://www.rnc.blb.gov/ssalur/www/Research3.html

  9. The Punch-Through Jet

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

  11. Punch – Through Jet II • v=0.999 • t=4.5/v fm • Mach cone for • sound waves • Diffusion wake

  12. Punch – Through Jet III BB et al., Phys. Rev. C 79, 034902 (2009) • Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity • pT = 5 GeV • Energy Flow Distribution • Diffusion wake causes • peak in jet direction • Assuming: Particles in subvolume will be emitted into the same direction

  13. The Stopped Jet

  14. Stopped Jet I • Applying a static medium and an ideal Gas EoS for massless gluons • Maximal fluid response • Assume: Near-side jet is not modified by medium BB et al., Phys. Rev. C 79, 034902 (2009) • Jet decelerating from v=0.999 • according to Bethe-Bloch formalism • Bragg Peak • adjusts path length • Simplest back-reaction from the medium

  15. Stopped Jet II • t=4.5/v fm BB et al., Phys. Rev. C 79, 034902 (2009) • pT = 5 GeV BB et al., Phys. Rev. C 79, 034902 (2009) • Diffusion wake causes • peak in jet direction

  16. Stopped Jet III • Jet stops after t=4.5/v fm BB et al., Phys. Rev. C 79, 034902 (2009) • tFO=4.5/v fm • tFO=6.5/v fm • tFO=8.5/v fm • Diffusion wake still present • Vorticity conservation

  17. Mechanisms of Energy Loss

  18. Diffusion Wake contribution • Mach cone in coordinate space S. Gubser et al., Phys. Rev. Lett. 100, 012301 (2008) Jets in AdS/CFT I • Pointing vector perturbation P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008) • Attention: No clear Mach cone signal • Energy density perturbation

  19. Jets in AdS/CFT II • Non-Mach correlations • caused by Neck region J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)

  20. Mach cone in coordinate space Jets in pQCD I • Considering a static medium and linearized hydrodynamics • for a punch-though jet R. Neufeld et al, Phys. Rev. C 78, 041901 (2008) • Mach cone signal & Diffusion Wake

  21. Mach cone in coordinate space Jets in pQCD II • Contour plots of magnitude of perturbed momentum density R. Neufeld et al., Phys. Rev. C 79, 054909 (2009) • Strong flow in jet direction

  22. t=4.5/v fm BB et al., Phys. Lett. B 675, 340 (2009) Heavy Quark Jets in pQCD vs AdS/CFT I • Idea: Compare weakly and strongly coupled models • Using heavy quark punch-through jet • 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 • pQCD: Neufeld et al. source for a heavy quark Neufeld et al, Phys. Rev. C 78, 041901 (2008) • AdS/CFT: Stress tables provided by S. Gubser, A. Yarom and S. Pufu with

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

  24. The Expanding Medium

  25. L. Satarov et al, Phys. Lett. B 627, 64 (2005) Expanding Medium I • Experimental results based • on many events • b=0 • Consider different jet paths A. K. Chaudhuri, Phys. Rev. C 75, 057902 (2007) , A. K. Chaudhuri, Phys. Rev. C 77, 027901 (2008) • Apply Glauber initial conditions and an ideal Gas EoS for massless gluons • Focus on radial flow contribution

  26. Etot = 5 GeV • Jet 150 Expanding Medium II • Jet deposition stopped • Etot = 5 or 10 GeV pTtrig = 3.5 and 7.5 GeV • T < Tcrit = 130 MeV • Isochronous Cooper-Frye Freeze-out • when Tall cells < Tcrit = 130 MeV • Two-particle correlation: f(f) represents the near-side jet Normalized, background-subtracted Cooper-Frye Freeze-out at mid-rapidity

  27. Expanding Medium III BB et al., arXiv:0907.2516 [nucl-th] • Etot = 5 GeV pTtrig = 3.5 GeV • broad away-side peak • double peaked structure • due to • non-central jets PHENIX, Phys. Rev. C 77, 011901 (2008)

  28. Expanding Medium IV • Etot = 10 GeV pTtrig = 7.5 GeV • broad away-side peak • double peaked structure • due to • non-central jets • Strong impact of the Diffusion wake • Causes smaller dip for pT=2 GeV PHENIX, Phys. Rev. C 77, 011901 (2008)

  29. Expanding Medium V • Etot = 5 GeV pTtrig = 3.5 GeV • broad away-side peak • broad away-side peak Pure energy deposition No conical distribution in expanding medium Jet 180: No peaks on away-side

  30. Summary • Diffusion wake dominates the freezeout distribution in a static medium • Different impact of pQCD and AdS/CFT source terms • Radial flow affects the results by deflecting Mach cones and interacting with the Diffusion wake • Diffusion wake contribution depends on path length of the jet • Away-side peaks: non-central jets have to be included • Pure energy deposition: No conical structure in expanding medium • always created if dM/dx > threshold • effect of the Neck region • clear difference between static & expanding medium • non-linear hydrodynamics is fundamental for • quantitative studies of jets in medium

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