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

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

3. Jet Propagation F. Wang, QM06 

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

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

6. Origin of Sideward Peaks

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

8. Hydrodynamical Approach

9. (3+1)d Hydrodynamik Assume: Near-side jet not influenced by medium Assume: Near-side jet not influenced by medium Ideal Gas EoS Ideal Gas EoS Implement a jet that... Implement a jet that... deposits energy and momentum within  deposits energy and momentum within 0.5 fm/c 0.5 fm/c  in a spherically expanding medium Use the Frankfurt (3+1)d ideal hydrodynamical code 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 Stopped hydrodynamical evolution after t=11.52 fm/c  Isochronous freeze-out  Cooper-Frye formula Considered a gas of  and  Considered a gas of  and  Using the Share program Using the Share program  for a 50 3 grid  and 10 events

13. Freeze-out Results  Jet Signal More particles are produced Particles with p x enhanced

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

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

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

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

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

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

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

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

22. Backup

23. SHASTA Solves finite difference versions of Solves finite difference versions of via the method of time-step splitting (operator splitting) 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)  1 =  ±     =  ±       = { 0 ±±±± 2 J. Ulery [STAR Collaboration], arXiv:0704.0224v1

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

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

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

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

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