Transcript Jet Energieverlust in Schwerionenkollisionen

Mach Cone Studies with 3D
Hydrodynamics
Barbara Betz
Institut für Theoretische Physik
Johann Wolfgang Goethe-Universität
Frankfurt am Main
NCRH2007 Frankfurt, 18. April 2007
Contents
I.
Introduction
•
Jet Quenching
•
Two and Three-Particle Correlation
II.
(3+1)d hydrodynamical approach
•
Jet Implementation
•
Jet Evolutions
•
Freeze-out
III.
Conclusion
Jet Propagation
Df
F. Wang, QM06
Df
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
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
Origin of Sideward Peaks
Three-Particle Correlation
Au+Au central 0-12%
Df1
Df2
Δf2
Δf1
J. Ulery [STAR Collaboration],
arXiv:0704.0224v1
Hydrodynamical Approach
(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
Ideal Gas EoS
t = 11.52 fm/c
Creation of a bow shock
Freeze-out
Giorgio Torrieri
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
Freeze-out Results
 Jet Signal
More particles are produced
Particles with px enhanced
Two-Particle Correlation
 Clear Jet Signal
 No Mach Cone
Three-Particle Correlation
Medium without jet
Medium with jet
Rectangular Nucleus Approach
• Implement a jet that ...
 deposits energy and
momentum within
1 fm/c


into a static,
homogeneous medium
Ideal Gas EoS
Vortices
 Smoke Rings
t = 11.52 fm/c
• Jet Signal
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
Discontinuous Energy Loss
t = 7.2 fm/c
 Clear Jet Signal
 Clear Mach Cone Signal
Conclusion
Two- and Three-Particle Correlation
I.
•
•
•
Sideward peaks appear and reflect
interaction of jet with medium and
emission angle of Mach Cone
Hydrodynamical approach
with Freeze-out
II.
•
•
•
Ideal Gas EoS
Jet visible independent of nature of
energy deposition
Clear Mach Cone appears in case of
discontinous energy deposition
Open Problems
I.
Influence of the background
II.
Evolution of a fast projectile
III.
Freeze-out for “rectangular nucleus
approach”
Backup
SHASTA
• Solves finite difference versions of
• via the method of time-step splitting (operator splitting)
 sequentially solving
Three-Particle Correlation
p
p
F. Wang [STAR Collaboration],
Nucl. Phys. A 774, 129 (2006)
J. Ulery [STAR Collaboration],
arXiv:0704.0224v1
Df1 = p ± 
Df1Df2
Df2 =p±
2
=
{
0
±
Mach Cone
Speed of Sound
Emission Angle of the Mach Cones
cos θ =
cs
vjet
~ 60 – 90°
F. Wang, QM06
• vjet depends on the mass of the leading quarks
 massless QGP:
 hadronic matter:
cs ~ 0.57
θ = 1.0 rad
cs ~ 0.3
θ = 1.3 rad
 1st order phase transition: cs ~ 0
θ = 1.5 rad
Break-up of the Mach Cone
t = 7.2 fm/c
Energy Distribution


Jet correlations in
p+p collisions:
Back-to-back peaks
appear.
Energy Distribution


Jet correlations in
central Au+Au
collisions:
Away-side jet
disappears for
particles with pt > 2
GeV/c
Energy Distribution


Jet correlations in
central Au+Au
collisions:
Away-side jet
(re)appears for
particles with pT >
0.15 GeV/c.