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Jet Propagation and Mach Cones
In (3+1)d Ideal Hydrodynamics
Barbara Betz,
Miklos Gyulassy, Dirk Rischke, Horst Stöcker and Giorgio Torrieri
Quark Matter 2008, Jaipur, India
Outline
I.
II.
Motivation: Jets in heavy-ion collisions
Jets in (3+1)d ideal hydrodynamics
•
Different energy-momentum deposition models

Particle Correlation Pattern
III. Conclusions & Outlook
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
2
Jet Quenching & Medium Response
• Jet suppression:
signal for QGP
• Re-appearance of the
away-side for low and
intermediate pTassoc
4 < pTtrigger < 6 GeV/c
pTassoc > 2 GeV/c
STAR PRL 91 (2003) 072304
4 < pTtrigger < 6 GeV/c
Au+Au / p+p
s= 200 GeV
PHENIX arXiv:0705.3238 [nucl-ex]
0.15 < pTassoc < 4 GeV/c
STAR, Nucl. Phys. A774, 129 (2006)
• Peaks reflect interaction of jet with medium
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Jets and Deposition Scenarios
 Solve numerically (3+1)d ideal hydrodynamics:
μ Τ  S
μυ
υ
 Source term Sυ given by jet energy loss
 Different models describing jet energy loss
R. Baier et al., Nucl. Phys. B438, 291 (1997)
M. Gyulassy et al., Nucl. Phys. B571, 197 (2000)
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006), arXiv: 0705.1352 [hep-ph]
H. Liu et al., PRL 97, 182301 (2006)
A. Majumder et al., PRL 99, 192301 (2007)
T. Renk et al., Phys. Rev. C75, 054910 (2007)
G.-Y. Qin et al., Phys. Rev. C76, 064907 (2007)
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Deposition Scenarios in Hydro
We use:
τf
υ
dP (4)  
S 
δ (x - x ()) d
dτ
τi
υ
x ()  x0  ujet

P  (E,M)
υ
a)
b)
c)
Pure energy deposition
Pure momentum deposition
Energy and momentum deposition
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Jets in (3+1)d Ideal Hydro
 Neglect near-side jet
 Study jet evolution in a homogeneous, non–
expanding background
• Bag model EoS for QGP
• Energy-momentum deposition for 0  t  5.6fm/c
 Isochronous freeze-out at t  7.2 fm/c
d3 N
μ
E 3   p dσμ f(x,p)
dp
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Pure Energy Deposition I
dE
GeV
 1.4
dx
fm
Need high–pT cuts
Otherwise thermal
smearing washes out
signal due to high
background temperature
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Pure Energy Deposition II
dE
GeV
 2.7
dx
fm
Higher value for dE /dx
signal seen already
for smaller pT
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Pure Energy Deposition III
dE
GeV
 9.0
dx
fm
Cone–like structure
for small–pT cuts
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Pure Energy Deposition IV
• Pure Energy Deposition
– Mach cone pattern
• More pronounced:
– higher dE/dx or pT
– consistent with J. C.-S. et al.
1  p T  2 GeV/c
dE
GeV
 1.4
dx
fm
0.2  p T  1 GeV/c
2  p T  3 GeV/c
3  p T  4 GeV/c
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Pure Momentum Deposition
dM
GeV
 1.4
dx
fm
Diffusion wake causes
• Disappearance of Mach
cone–like pattern
• peak in forward direction
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Energy & Momentum Deposition I
Mjet
E jet
0
02 / 08 / 2008
dE
GeV
 1.4
dx
fm
Mjet
E jet
1

2
Barbara Betz
Quark Matter 2008, Jaipur, India
Mjet
E jet
1
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Energy & Momentum Deposition II
dE
GeV
 1.4
dx
fm
2  p T  5 GeV/c
dE
GeV
 12.6
dx
fm
• Mach cone–like pattern
for dM/dx  dE/dx
dE
GeV
2
dx
fm
J. Casalderrey-Solana et al.
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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Conclusions & Outlook
Mach cone correlation pattern
- appears only if dM/dx  dE/dx
otherwise: Diffusion wake kills the Mach
cone–like pattern
- is not visible for cuts similar to experiment if
dE/dx  9 GeV/fm
Further investigations:
• realistic energy–momentum deposition scenario
• expanding medium
02 / 08 / 2008
Barbara Betz
Quark Matter 2008, Jaipur, India
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