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Jet Propagation and Mach-Cone Formation in (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), - PowerPoint PPT Presentation
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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?
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
5 15/09/2009
The Theory Part
Barbara Betz Trento Workshop on Flow and Dissipation
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
,
, ,
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
9 15/09/2009
The Punch-Through Jet
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
13 15/09/2009
The Stopped Jet
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
17 15/09/2009
Mechanisms of Energy Loss
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
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
Barbara Betz Trento Workshop on Flow and Dissipation
24 15/09/2009
The Expanding Medium
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
26 15/09/2009
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
Barbara Betz Trento Workshop on Flow and Dissipation
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)
Barbara Betz Trento Workshop on Flow and Dissipation
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)
pTTtrig trig = 7.5 GeV
Barbara Betz Trento Workshop on Flow and Dissipation
29 15/09/2009
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
pTTtrig trig = 3.5 GeV
Barbara Betz Trento Workshop on Flow and Dissipation
30 15/09/2009
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
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