Jet Propagation and Mach ConesIn (3+1)d Ideal Hydrodynamics

Barbara Betz,Miklos Gyulassy, Dirk Rischke, Horst Stöcker and Giorgio

Torrieri

Quark Matter 2008, Jaipur, IndiaQuark Matter 2008, Jaipur, India

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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Outline

I. Motivation: Jets in heavy-ion collisions

II. 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

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Jet Quenching & 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 GeV/c

STAR PRL 91 (2003) 072304

• Jet suppression: signal for QGP

4 < pTtrigger < 6 GeV/c

pTassoc > 2 GeV/c

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:

υμυμ 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)

υS

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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We use:

a) Pure energy depositionb) Pure momentum depositionc) Energy and momentum deposition

Deposition Scenarios in Hydro

d))(x-(xδdτ

dPS (4)

τ

τ

υυ

f

i

)M(E,Pυ

jet0 ux)(x

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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• Energy-momentum deposition for

Jets in (3+1)d Ideal Hydro

• Bag model EoS for QGP

p)f(x,dσpdp

NdE μ

μ3

3

fm/c7.2t

Neglect near-side jet

Study jet evolution in a homogeneous, non– expanding background

Isochronous freeze-out at

fm/c5.6t0

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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Pure Energy Deposition I

fmGeV

1.4dxdE

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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fmGeV

2.7dxdE

Higher value for

signal seen already for smaller pT

Pure Energy Deposition II

dE/dx

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

9

fmGeV

9.0dxdE

Pure Energy Deposition III

Cone–like structure for small–pT cuts

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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• More pronounced:– higher or pT

– consistent with J. C.-S. et al.

Pure Energy Deposition IV• 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

1.4dxdE

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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fmGeV

1.4dxdM

Diffusion wake causes• Disappearance of Mach

cone–like pattern• peak in forward direction

Pure Momentum Deposition

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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Energy & Momentum Deposition I

fmGeV

1.4dxdE

1E

M

jet

jet 0E

M

jet

jet 21

E

M

jet

jet

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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• Mach cone–like pattern for

J. Casalderrey-Solana et al.

Energy & Momentum Deposition II

J. Casalderrey-Solana et al., Nucl. Phys. A 774, 577 (2006)

fm

GeV2

dx

dE

dE/dx dM/dx

GeV/c 5 Tp2

fm

GeV12.6

dx

dE

fmGeV

1.4dxdE

02 / 08 / 2008 Barbara Betz Quark Matter 2008, Jaipur, India

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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

Conclusions & Outlook

dE/dxdM/dx

GeV/fm9dE/dx

Further investigations:

• realistic energy–momentum deposition scenario• expanding medium