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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
05 / 02 / 08 Barbara Betz 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
• Peaks reflect interaction of jet with medium
• Re-appearance of the away-side for low and intermediate pT
assoc
PHENIX arXiv:0705.3238 [nucl-ex]
Au+Au / p+p
= 200 GeVs
STAR, Nucl. Phys. A774, 129 (2006)
4 < pTtrigger < 6 GeV/c
0.15 < pTassoc < 4 eV/c
• Jet suppression: signal for QGP
STAR PRL 91 (2003) 072304
4 < pTtrigger < 6 GeV/c
pTassoc > 2 GeV/c
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
Solve numerically (3+1)d ideal hydrodynamics:
νμνμ SΤ
Source term 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]
νS
Jets & Deposition Scenarios
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
We use:
Written non-covariantly
Different deposition scenarios
τττ
τ
νν d))(x-(x
ddP
S μμ(4)f
i
δτ
)M(E,P
ν
ττ μjet
μ0
μ ux)(x
Deposition Scenarios Hydro
,0,0
dxdM
,dxdE
2σ
)xr(exp
σ)2(
1S
2
2
3
πν
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
• Energy-momentum deposition for
• Bag model EoS for QGP
p)f(x,dσppd
dNE μ
μ3
fm/c7.2t
Neglect near-side jet
Study jet evolution in a homogeneous, non– expanding background
Isochronous freeze-out at
fm/c4.5t0
Jets in (3+1)d Ideal Hydro
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
fmGeV
10dxdM
dxdE
Peak in jet direction Are we done?
Source unknownDistribution function unknown
On-Shell Deposition I
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
Diffusion wake causes• peak in forward direction J. Casalderrey-Solana et al.
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
fm
GeV2
dx
dE
GeV/c 5 Tp2
fm
GeV12.6
dx
dE
fmGeV
10dxdM
dxdE
On-Shell Deposition II
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
On-shellness:
Energy-Momentum Relation
222 mpE
/2ΔpΔx Heisenberg’s uncertainty relation:
Radiative energy loss
small largeΔx Δp
2
Δm
22222 mΔp2pΔppm)Δp(pE2
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
fmGeV
10dxdE
0dxdM
dxdE
dxdM
dxdE
21
dxdM
Off-Shell Deposition I
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
Mach cone–like pattern for dE/dx dM/dx
fmGeV
1.4dxdE
Off-Shell Deposition II
Transverse momentum loss
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
fmGeV
10dxdE
Cone–like structure
Pure Energy Loss I
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
fmGeV
1.4dxdE
Need high–pT cuts Otherwise thermal
smearing washes out signal due to high background temperature
Pure Energy Loss II
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
• More pronounced:– higher or pT
– consistent with J. C.-S. et al.
• Pure Energy Deposition– Mach cone pattern
J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)
dE/dx
GeV/c 3 Tp2
GeV/c 2 Tp1
GeV/c 4 Tp3
GeV/c 1 Tp0.2
fmGeV
10dxdE
Pure Energy Loss III
05 / 02 / 08 Barbara Betz Yale Columbia Day, Yale University
Mach cone correlation pattern
- appears only if otherwise: Diffusion wake kills the Mach
cone–like pattern
- is not visible for cuts similar to experiment if
dE/dxdM/dx
GeV/fm10dE/dx
Conclusions
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?