Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics

Jet Propagationand Mach-Cone Formationin (3+1)-dimensional Ideal

Hydrodynamics

Barbara Betz

Thanks goes to:Miklos Gyulassy, Igor Mishustin, Jorge Noronha,

Dirk Rischke, Philip Rau, Horst Stöcker, and Giorgio Torrieri

Phys. Lett. B 675, 340 (2009), Phys. Rev. C 79, 034902 (2009), arXiv: 0907.2516 [nucl-th]

Barbara Betz Trento Workshop on Flow and Dissipation

2 15/09/2009

Explore The Matter Created in HIC

Data described by hydrodynamics

Jets are suppressed

System is dense and opaque

P. Romatschke et al., Phys. Rev. Lett. 99,172301 (2007)

Fluid behaviour

STAR, Phys. Rev. Lett. 91 (2003) 072304

4 < pTtrigger < 6 GeV/c

pTassoc > 2 GeV/c

Can energy lost by jets tell us something about medium properties?


3 15/09/2009

PHENIX, Phys. Rev. C 77, 011901 (2008)

Au+Au / p+p = 200 GeVs

• Redistribution of energy to lower pT-particles Generation of Mach cone pattern

• Re-appearance of the away-side for low and intermediate pT

assoc

• Mach cone angle sensitive to EoS:

STAR, Nucl. Phys. A 774, 129 (2006)

4 < pTtrigger < 6 GeV/c

0.15 < pTassoc < 4 GeV/c

Reflect interaction of jet with medium

Jet - Studies in HIC I


4 15/09/2009

Experimental data showsuperposition of Mach conestructure and deflected jets

J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007)

Deflected jet Mach Cone

Jet - Studies in HIC II• Is the double-peaked structure due to a Mach cone formation?

ptrigT=3 – 4 GeV, passoc

T=1 – 2 GeV


5 15/09/2009

The Theory Part


6 15/09/2009

Ideal Hydrodynamics Medium created in a HIC can be described using hydrodynamics

• Hydrodynamics represents (local) conservation of

energy-momentum

(local) charge

• For ideal hydrodynamics in local thermodynamical equilibrium

• Equation of State

,

, ,


7 15/09/2009

Modelling of Jets

Jet deposition mechanism unclear

Jets can be modelled using hydrodynamics:

STAR PRL 95 (2005) 152301

not the source term of the jet

residue of energy and momentum given by the jet


8 15/09/2009

Cooper-Frye Freeze-out:

The Caveat: Freeze-out Prescription

• Assumption of isochronous/isothermal freeze-out • No interaction afterwards

mainly flow driven

http://www.rnc.blb.gov/ssalur/www/Research3.html


9 15/09/2009

The Punch-Through Jet


10 15/09/2009

t=4.5/v fm v=0.999

Punch – Through Jet I Applying a static medium and an ideal Gas EoS for massless gluons

dM dE GeV1.5dt dt fm= =dE GeV dM GeV1.5 , 0dt fm dt fm= =

Maximal fluid response

BB et al., Phys. Rev. C 79, 034902 (2009)

Assume: Near-side jet is not modified by medium


11 15/09/2009

t=4.5/v fm v=0.999

Punch – Through Jet II

dM dE GeV1.5dt dt fm= =dE GeV dM GeV1.5 , 0dt fm dt fm= =

Mach cone forsound waves Diffusion wake


12 15/09/2009

Punch – Through Jet III

Diffusion wake causes peak in jet direction

Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity

Energy Flow Distribution

Assuming: Particles in subvolume will be emitted into the same direction

pT = 5 GeV

BB et al., Phys. Rev. C 79, 034902 (2009)


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The Stopped Jet


14 15/09/2009

Stopped Jet IApplying a static medium and an ideal Gas EoS for massless gluons

Assume: Near-side jet is not modified by mediumMaximal fluid response

Jet decelerating from v=0.999according to Bethe-Bloch formalism

Simplest back-reaction from the medium

Bragg Peak

adjusts path length

BB et al., Phys. Rev. C 79, 034902 (2009)


15 15/09/2009

Diffusion wake causes peak in jet direction

pT = 5 GeV

BB et al., Phys. Rev. C 79, 034902 (2009)

dE dM GeV(0) v (0) 1.5dt dt fm= =

dE GeV dM GeV(0) 1.5 (0) 0dt fm dt fm= =

BB et al., Phys. Rev. C 79, 034902 (2009)

Stopped Jet II t=4.5/v fm


16 15/09/2009

Stopped Jet III • Jet stops after t=4.5/v fm

dE GeV(0) 1.5dt fmdM GeV(0) 0dt fm

=

=

dE GeV(0) 1.5dt fmdM GeVv (0) 1.5dt fm

=

=

Vorticity conservationtFO=4.5/v fm tFO=6.5/v fm tFO=8.5/v fm

Diffusion wake still present

BB et al., Phys. Rev. C 79, 034902 (2009)


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Mechanisms of Energy Loss


18 15/09/2009

Diffusion Wake contribution

Jets in AdS/CFT I

P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008)

S. Gubser et al., Phys. Rev. Lett. 100, 012301 (2008)

Pointing vector perturbation

Energy density perturbationAttention: No clear Mach cone signal


19 15/09/2009

Non-Mach correlations caused by Neck region

Jets in AdS/CFT II

J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)


20 15/09/2009

Jets in pQCD I

R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)

Considering a static medium and linearized hydrodynamicsfor a punch-though jet

Mach cone signal & Diffusion Wake


21 15/09/2009

Jets in pQCD II

1s 4

= 3

s 4

= 6

s 4

=

Contour plots of magnitude of perturbed momentum density

Strong flow in jet direction

R. Neufeld et al., Phys. Rev. C 79, 054909 (2009)


22 15/09/2009

Heavy Quark Jets in pQCD vs AdS/CFT I

Idea: Compare weakly and strongly coupled models

Using heavy quark punch-through jet

pQCD: Neufeld et al. source for a heavy quark

AdS/CFT: Stress tables provided by S. Gubser, A. Yarom and S. Pufu with

Applying ideal hydrodynamics for a staticmedium and an ideal gas EoS of masslessgluons

Assume that the near-side jet is not modified by the medium

/s=1/(4 )

BB et al., Phys. Lett. B 675, 340 (2009)

t=4.5/v fm

Neufeld et al, Phys. Rev. C 78, 041901 (2008)


23 15/09/2009

No Mach-like peaks:

Isochronous freezeout needed to compare pQCD and AdS/CFT

Normalized, background-subtracted isochronous Cooper-Frye at mid-rapidity

pT = 3.14 GeVStrong influence of the Neck regionJ. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)

BB et al., Phys. Lett. B 675, 340 (2009)

Heavy Quark Jets in pQCD vs AdS/CFT II


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The Expanding Medium


25 15/09/2009

Expanding Medium I

Consider different jet paths

b=0

• Apply Glauber initial conditions and an ideal Gas EoS for massless gluons• Focus on radial flow contribution

Experimental results based on many events

A. K. Chaudhuri, Phys. Rev. C 75, 057902 (2007) ,

A. K. Chaudhuri, Phys. Rev. C 77, 027901 (2008)

L. Satarov et al, Phys. Lett. B 627, 64 (2005)


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Expanding Medium II• Jet deposition stopped

Etot = 5 or 10 GeVpTT

trig trig = 3.5 and 7.5 GeV

T < Tcrit = 130 MeV

• Isochronous Cooper-Frye Freeze-out when Tall cells < Tcrit = 130 MeV

• Two-particle correlation:

f() represents the near-side jet

Normalized, background-subtractedCooper-Frye Freeze-out at mid-rapidity

Jet 150

Etot = 5 GeV


27 15/09/2009

Expanding Medium IIIEtot = 5 GeV

broad away-side peak double peaked structure

due to non-central jets

pTTtrig trig = 3.5 GeV

BB et al., arXiv:0907.2516 [nucl-th]

PHENIX, Phys. Rev. C 77, 011901 (2008)


28 15/09/2009

Expanding Medium IV Etot = 10 GeV

Strong impact of the Diffusion wake

broad away-side peak double peaked structure

due to non-central jets

Causes smaller dip for pT=2 GeV PHENIX, Phys. Rev. C 77, 011901 (2008)



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Expanding Medium VEtot = 5 GeV

broad away-side peak broad away-side peak

Pure energy deposition No conical distribution in expanding mediumJet 180: No peaks on away-side



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Summary Diffusion wake dominates the freezeout distribution in a static

medium

Different impact of pQCD and AdS/CFT source terms

Radial flow affects the results by deflecting Mach cones and interacting with the Diffusion wake

Diffusion wake contribution depends on path length of the jet Away-side peaks: non-central jets have to be included Pure energy deposition: No conical structure in expanding

medium

always created if dM/dx > threshold

clear difference between static & expanding medium

effect of the Neck region

non-linear hydrodynamics is fundamental for quantitative studies of jets in medium

Jet Propagation and Mach-Cone Formation in (3+1)-dimensional Ideal Hydrodynamics

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