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Mach Cone Studies with 3D Hydrodynamics

Barbara Betz Institut für Theoretische Physik Johann Wolfgang Goethe-Universität Frankfurt am Main. Mach Cone Studies with 3D Hydrodynamics. NCRH2007 Frankfurt, 18. April 2007. Contents. Introduction Jet Quenching Two and Three-Particle Correlation (3+1)d hydrodynamical approach

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Mach Cone Studies with 3D Hydrodynamics

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  1. Barbara Betz Institut für Theoretische Physik Johann Wolfgang Goethe-Universität Frankfurt am Main Mach Cone Studies with 3D Hydrodynamics NCRH2007 Frankfurt, 18. April 2007

  2. Contents • Introduction • Jet Quenching • Two and Three-Particle Correlation • (3+1)d hydrodynamical approach • Jet Implementation • Jet Evolutions • Freeze-out • Conclusion

  3. Jet Propagation Df Df F. Wang, QM06

  4. Jet Quenching • Suppression of the away-side jets • in Au+Au collisions • 4 < pT < 6 GeV/c • pTassoc > 2 GeV/c • Compared to p+p collisions J. Adams [STAR Collaboration], Phys. Rev. Lett. 91 072304 (2003) Jet Quenching

  5. Two-Particle Correlation • Redistribution of energy to low pT-particles: • Sideward peaks • 4 < pT < 6 GeV/c • 0.15 < pTassoc < 4 GeV/c F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006) • Peaks reflect interaction of jet with medium

  6. Origin of Sideward Peaks

  7. Three-Particle Correlation Au+Au central 0-12% Δ2 Df1 Df2 Δ1 J. Ulery [STAR Collaboration], arXiv:0704.0224v1

  8. Hydrodynamical Approach

  9. (3+1)d Hydrodynamik • Assume: Near-side jet not influenced by medium • Implement a jet that ... • deposits energy and momentum within 0.5 fm/c • in a spherically expanding medium • Ideal Gas EoS • Use the Frankfurt (3+1)d ideal hydrodynamical code

  10. Ideal Gas EoS t = 11.52 fm/c Creation of a bow shock

  11. Freeze-out Giorgio Torrieri

  12. Freeze-out • Stopped hydrodynamical evolution after t=11.52 fm/c • Isochronous freeze-out • Cooper-Frye formula • Considered a gas of p and r • Using the Share program • for a 503 grid • and 10 events

  13. Freeze-out Results • Jet Signal More particles are produced Particles with px enhanced

  14. Two-Particle Correlation • Clear Jet Signal • No Mach Cone

  15. Three-Particle Correlation Medium without jet Medium with jet

  16. Rectangular Nucleus Approach • Implement a jet that ... • deposits energy and momentum within 1 fm/c • into a static, homogeneous medium • Ideal Gas EoS

  17. Vortices • Smoke Rings t = 11.52 fm/c • Jet Signal

  18. Discontinuous Energy Loss • Implement a jet that ... • deposits energy of 2 GeV • in equal time intervals of Dt = 1.6 fm/c • into a static, homogeneous medium • Ideal Gas EoS

  19. Discontinuous Energy Loss t = 7.2 fm/c • Clear Jet Signal • Clear Mach Cone Signal

  20. Conclusion • Two- and Three-Particle Correlation • Sideward peaks appear and reflect • interaction of jet with medium and • emission angle of Mach Cone • Hydrodynamical approach with Freeze-out • Ideal Gas EoS • Jet visible independent of nature of energy deposition • Clear Mach Cone appears in case of discontinous energy deposition

  21. Open Problems • Influence of the background • Evolution of a fast projectile • Freeze-out for “rectangular nucleus approach”

  22. Backup

  23. SHASTA • Solves finite difference versions of • via the method of time-step splitting (operator splitting) • sequentially solving

  24. Three-Particle Correlation   F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006) J. Ulery [STAR Collaboration], arXiv:0704.0224v1 1 = ± =±  { 0 = ± 2

  25. Mach Cone Speed of Sound Emission Angle of the Mach Cones cs cos θ = ~ 60 – 90° vjet F. Wang, QM06 • vjet depends on the mass of the leading quarks θ = 1.0 rad • massless QGP: cs ~ 0.57 • hadronic matter: cs ~ 0.3 θ = 1.3 rad • 1st order phase transition: cs ~ 0 θ = 1.5 rad

  26. Break-up of the Mach Cone t = 7.2 fm/c

  27. Energy Distribution • Jet correlations in p+p collisions: • Back-to-back peaks appear.

  28. Energy Distribution • Jet correlations in central Au+Au collisions: • Away-side jet disappears for particles with pt > 2 GeV/c

  29. Energy Distribution • Jet correlations in central Au+Au collisions: • Away-side jet (re)appears for particles with pT > 0.15 GeV/c.

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