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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 Disputationsvortrag Johann Wolfgang Goethe-Universität Frankfurt am Main 13/10/2009. Phys. Lett. B 675 , 340 (2009), Prog. Part. Nucl. Phys. 62 , 556 (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 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. The QCD Phase Diagram • proton • 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 hadronic phase and freeze-out expanding fireball initial state pre-equilibrium hadronization S. Bass, Talk Quark Matter 2001

  3. The Expanding Medium • From first principles, it is unclear if medium is … • „dust“ • fluid • Particles don‘t interact, • expansion independent • of initial shape • Particles interact, • expansion determined • by density gradient • Hydrodynamics: azimuthal anisotropy of • emitted particles, parametrized by v2 • Data described by hydrodynamics • Small • Medium behaves like an almost • ideal fluid P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99,172301 (2007)

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

  5. 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 II • 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

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

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

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

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

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

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

  13. Etot = 5 GeV • Jet 150 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 • Two-particle correlation (Tfreeze-out < Tcrit = 130 MeV): represents near-side jet

  14. Expanding Medium II BB et al., Nucl. Phys. A in press (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)

  15. 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. Backup

  17. 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

  18. Punch – Through Jet II 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

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

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

  21. Punch – Through vs Stopped Jet BB et al., Phys. Rev. C 79, 034902 (2009) • pT = 5 GeV • pT = 5 GeV • Punch-Through Jet • Stopped Jet • Similar freeze-out patterns

  22. Punch – Through Jet: Velocity Scan • t=4.5/v fm

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

  24. The Diffusion Wake G. Burau, Genua Harbour, September 2008 • The diffusion wake exists!

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

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

  27. Stopped Jet • 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

  28. Stopped Jet • Larger impact of thermal smearing • Diffusion wake causes • peak in jet direction BB et al., Phys. Rev. C 79, 034902 (2009) • tFO=4.5/v fm • tFO=6.5/v fm • tFO=8.5/v fm

  29. Different Contributions BB et al., Phys. Rev. C 79, 034902 (2009) • EMach 53.9% PxMach 6.5% • EDiff -12.3% PxDiff 18.7% • ENeck 57.4% PxNeck 73.7% • EHead 1.0% PxHead 1.0% • t=4.5/v fm • pT =2. 5 GeV

  30. Energy-Momentum Relation • general:

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

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

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

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

  35. 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

  36. 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

  37. pQCD Source Term I • Idea: External color field generated by fast parton propagating through QGP • with • Lorentz forced • considered to lowest order in coupling g • Since

  38. pQCD Source Term II • For a parton moving with v=const. and omitting dielectric screening: • with

  39. pQCD Source Term III • For ultraviolett and infrared cut-off: • Ep energy of fast parton

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

  41. 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

  42. 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)

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

  44. Expanding Medium • Jet 90 • Jet 120 • Jet 180 • Jet 150

  45. Expanding Medium • Jet 120 • Jet 150 • Jet 180

  46. Expanding Medium • Etot = 5 GeV pTtrig = 3.5 GeV • broad away-side peak • double peaked structure PHENIX, Phys. Rev. C 77, 011901 (2008)

  47. Expanding Medium • 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)

  48. Expanding Medium • 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

  49. Expanding Medium • Etot = 5 GeV • Etot = 5 GeV • Etot = 10 GeV pTtrig = 3.5 GeV pTtrig = 3.5 GeV pTtrig = 7.5 GeV • en. and mom. loss • en. and mom. loss • pure energy loss

  50. Expanding Medium • Etot = 4.3 GeV pTtrig = 3.0 GeV • broad away-side peak • broad away-side peak

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