Transcript Folie 1

Jet Propagation &
Mach Cone Evolution
in (3+1)d Ideal Hydrodynamics
Barbara Betz,
Miklos Gyulassy, Dirk Rischke, Horst Stöcker and Giorgio Torrieri
05 / 02 / 08
Yale Columbia Day, Yale University
Outline
I.
Motivation: Jets in heavy-ion collisions
II.
Jets in (3+1)d ideal hydrodynamics
•
Different energy-momentum deposition
scenarios

Particle Correlation Pattern
III. Conclusions, Outlook & Open Questions
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Jets & 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=
PHENIX arXiv:0705.3238 [nucl-ex]
0.15 < pTassoc < 4 eV/c
200 GeV
STAR, Nucl. Phys. A774, 129 (2006)
• Peaks reflect interaction of jet with medium
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Jets & Deposition Scenarios
 Solve numerically (3+1)d ideal hydrodynamics:
μΤ
μν
S
ν
ν
 Source term S 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)
R. Neufeld et al., arXiv: 0802.2254 [hep-ph]
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Deposition Scenarios Hydro
We use:
τf
ν
S 

dP
ν
dτ

ν
P  (E, M )
δ
(4)
μ
μ
(x - x ( τ )) d τ
μ
μ
τi
Written non-covariantly
ν
S 
1
( 2 π σ)
3
  2
 ( r  x )   dE
dM



exp 
,
,0,0 

2


dx
2σ


  dx
Different deposition scenarios
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
μ
x ( τ )  x 0  u jet τ
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 
 Isochronous freeze-out at t  7.2 fm/c
E
dN
3
d p
05 / 02 / 08

μ
 p dσ μ f(x, p)
Barbara Betz
Yale Columbia Day, Yale University
t  4.5 fm/c
On-Shell Deposition I
dE
dx

dM
dx
Peak in jet direction
 10
GeV
fm
Are we done?
Source unknown
Distribution function unknown
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
On-Shell Deposition II
dE
dx

dM
dx
 10
GeV
2  p
fm
T
 5 GeV/c
dE
Diffusion wake causes
• peak in forward direction
J. Casalderrey-Solana et al.
dx
 12.6
GeV
fm
dE
dx
2
GeV
fm
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Energy-Momentum Relation
2
2
2
On-shellness: E  p  m
Heisenberg’s uncertainty relation:
Δx  Δp   /2
Radiative energy loss
Δx small
2
Δp
2
large
2
2
2
E  (p  Δp )  m  p  2p Δp  Δp  m
  
Δm
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
2
2
Off-Shell Deposition I
dM
dx

05 / 02 / 08
dE
dE
dx
dx
 10
GeV
dM
fm
dx

1 dE
dM
2 dx
dx
Barbara Betz
Yale Columbia Day, Yale University
0
Off-Shell Deposition II
dE
dx
 1.4
GeV
fm
Mach cone–like pattern for dM/dx  dE/dx
Transverse momentum loss
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Pure Energy Loss I
dE
dx
 10
GeV
fm
Cone–like structure
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Pure Energy Loss II
dE
dx
Need high–pT cuts
 1.4
GeV
fm
Otherwise thermal
smearing washes out
signal due to high
background temperature
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Pure Energy Loss III
• Pure Energy Deposition
– Mach cone pattern
• More pronounced:
– higher dE/dx or pT
– consistent with J. C.-S. et al.
1  p
0.2  p
2  p
3  p
T
T
T
T
 2 GeV/c
 1 GeV/c
 3 GeV/c
 4 GeV/c
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
dE
dx
 10
GeV
fm
Conclusions
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  10 GeV/fm
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University
Open Questions
& further investigations:
• energy–momentum deposition scenario
– Transverse momentum loss
– Spatial dependence
– Interaction of jet with medium
• expanding medium
– Radial flow
– Elliptic flow
Effect of disentangling?
• Neglecting near-side?
05 / 02 / 08
Barbara Betz
Yale Columbia Day, Yale University