Transcript Mach Cone Studies in (3+1)d Ideal Hydrodynamics

Mach Cone Studies in (3+1)d
Ideal Hydrodynamics
Barbara Betz,
Philip Rau, Dirk Rischke, Horst Stöcker, Giorgio Torrieri
Institut für Theoretische Physik
Johann Wolfgang Goethe-Universität
Frankfurt am Main
LHC Workshop CERN, 31. 5. 2007
Contents
I.
Introduction
•
Measured Two- and Three-Particle Correlations
II.
(3+1)d hydrodynamical approach
•
Jet Evolution
•
Two- and Three-Particle Correlations




III.
Different Energy and Momentum Deposition
15 GeV jet
30 GeV jet
1500 particles total multiplicity
Conclusion
Two-Particle Correlation
 Sideward peaks
 4 < pTtrig < 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
Three-Particle Correlation
Au+Au central 0-12%
D1
Δ2
D2
Δ1
J. Ulery [STAR Collaboration],
arXiv:0704.0224v1
Hydrodynamical Approach
(3+1)d Ideal Hydrodynamik
 Assume: Near-side jet not influenced by medium
• Bjorken cylinder
• initial radius r = 3.5 fm
• t0 = 1 fm/c
 Bag Model EoS with a 1st order phase transition
Energy Deposition
We compare:



15 GeV jet
30 GeV jet
1500 particles total multiplicity
Jet deposits its energy and momentum
•
•
within t = 1 fm/c
in equal time intervals
Energy and Momentum Deposition
within t = 1 fm/c
of a 15 GeV jet
http://waterocket.explorer.free.fr/images/bullet1.jpg
Jet Evolution
Creation of a bow shock
t = 6.4 fm/c
Momentum Distribution
t = 6.4 fm/c
Freeze-out
• Stopped hydrodynamical evolution after t=6.4 fm/c
 Isochronous freeze-out
 Cooper-Frye formula
• Considered a gas of p and r
• Using the Share program
 for a 503 grid
 and 40 events
Particle Correlations
 Clear Jet Signal
 No Mach Cone
Energy and Momentum Deposition
in equal time intervals
of a 15 GeV jet
A. Filippone, www.aerodyn.org/Acoustics/Sound/sound.html
Jet Evolution
Mach Cone like signal
t = 6.4 fm/c
Momentum Distribution
t = 6.4 fm/c
Particle Correlations
 Mach Cone like signal
Single and Multiple
Energy and Momentum Deposition
of a 30 GeV jet
Jet Evolution
multiple
single
energy and momentum deposition
bow shock
t = 6.4 fm/c
Momentum Distribution
single
multiple
energy and momentum deposition t = 6.4 fm/c
Two-Particle Correlation
multiple
single
energy and momentum deposition
 Jet Signal
Three-Particle Correlation
single
multiple
energy and momentum deposition
Conclusion
Two- and Three-Particle Correlation
I.
Sideward peaks appear and reflect
•
•
interaction of jet with medium
Hydrodynamical approach and Freeze-out
II.
•
•
Bag Model EoS
Bjorken-like expansion

Jet visible independent of nature of energy
deposition

Evolution of a Mach Cone depends on

Energy and Momentum deposition

Jet Energy
Backup
Jet Quenching

Suppression of the
away-side jets

in Au+Au collisions

4 < pTtrig < 6 GeV/c

pTassoc > 2 GeV/c

Compared to p+p
collisions
J. Adams [STAR Collaboration], Phys. Rev. Lett. 91
072304 (2003)
Jet Quenching
Freeze-out Results
single
deposition
Ejet = 15 GeV
 Jet Signal

Particles with px enhanced
High Energy
multiple
deposition
Ejet = 30 GeV
 Jet Signal
Origin of Sideward Peaks