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?