Jet Energy Loss and Mach Cones,Jet-Medium Interactions,Jets in Hydrodynamics
Barbara Betz
Thanks to: Miklos Gyulassy, Jorge Noronha, Dirk Rischke,
Giorgio Torrieri
Phys. Rev. C 79, 034902 (2009), Phys. Lett. B 675, 340 (2009),
Nucl. Phys. A 830, 777c (2009), arXiv:1005.5461
Towards a Consistent Picture of Mach Cones in Heavy-Ion Collisions
From the Static Medium toJet Reconstruction Algorithms
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The Medium created in a HIC
Data described by hydrodynamics
Small
P. Romatschke and U. Romatschke, Phys. Rev. Lett. 99,172301 (2007)
Medium behaves like an almost
ideal fluid
/s
IF the medium behaves like a fluid
Mach cones have to occurbecause of fluid dynamics
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Jet - Studies in HIC
• Generation of Mach cone pattern
Redistribution of energy to lower pT-particles
• 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 mediumPHENIX, Phys. Rev. C 77, 011901 (2008)
Au+Au / p+p
= 200 GeVs
H. Stöcker, Nucl. Phys. A 750, 121 (2005), J. Casalderrey-Solana et al. Nucl. Phys. A 774, 577 (2006)
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Jet - Medium Interaction
• First-order phase transition
• Expanding (2+1)d hydro (AZHYDRO)
• Quenched jet
• Isothermal Freeze-out
A. Chaudhuri and U. Heinz, Phys. Rev. Lett. 97, 062301 (2006)
Where does the double-peaked structurecome from?
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Extended Jet - Studies in HIC
STAR, arXiv: 1004.2377
see also PHENIX, Phys. Rev. C 77, 011901 (2008)
Position of away-sidepeaks does not changestrongly with pT
assoc
Not due toCherenkov gluonradiation
What happens to larger pT
trigger?
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Some Caveats
ZYAM (Zero Yield At Minimum):Can lead to a double-peaked structure
Two-source model:Can one assume that the correlationsfrom flow anisotropy and jets areuncorrelated? J. Ulery [STAR], PoS LHC07, 036 (2007)
How can one proof/disproof the two-source model?
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J. Ulery [STAR], Int. J. Mod. Phys. E 16, 2005 (2007)
ptrigT=3 – 4 GeV, passoc
T=1 – 2 GeV Three-particle correlations seem to
corroborate Mach cone idea
What’s the effect of ZYAM?
No agreement with 3-particle cumulant method C. Pruneau, Phys. Rev. C 79, 044907 (2009)
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Modelling of Jets
STAR, Phys. Rev. Lett. 95, 152301 (2005)
residue of energy and momentum given by the jet
• Assumption of isochronous/isothermal freeze-out
• No interaction afterwards
mainly flow driven
Conversion into particles Freeze-out:
Jets can be modelled using (ideal) hydrodynamics:
e+p v.
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Stopped Jet IApplying a static medium and an ideal Gas EoS for massless gluons
Assume: Near-side jet is not modified by medium
Maximal fluid response
Jet decelerating from v=0.999according to Bethe-Bloch formalism
a=-1.36 GeV/fm
Simplest back-reaction from the medium
Bragg Peak
adjusts path length
BB et al., Phys. Rev. C 79, 034902 (2009)
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Stopped Jet II
Mach cone forsound waves Diffusion wake
dE dM GeV(0) v (0) 1.5
dt dt fm= =
t=4.5/v fmdE GeV dM GeV
(0) 1.5 (0) 0dt fm dt fm
= =
BB et al., Phys. Rev. C 79, 034902 (2009)
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Stopped Jet III
Diffusion wake causespeak 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)
Any conclusions about deposition mechanism???
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Modelling Jets using …
Conclusion about Mach cones?
pQCD
AdS/CFT
P. Chesler and L. Yaffe, Phys. Rev. D 78, 045013 (2008)
R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)
Strongly-coupled theory
Pointing vector perturbation
Momentum density perturbationEnergy density perturbation
Energy density perturbation
Weakly-coupled theory
v=0.75
v=0.99955
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Non-Mach correlations
caused by Neck region
Jets in AdS/CFT
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
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Why linearized Hydro is not so good
Head wave pile-up- Non-linear hydrodynamics- Signal not well understood- Non-Mach cone angle
Source- Non-linear hydrodynamics- Non-thermalized
Diffusion Wake - Proportional to source- Not seen experimentally
Mach Cone- Linear hydrodynamics- Connected to EoS
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Heavy Quark JetsCompare weakly and strongly coupled models using heavy punch-through jet
pQCD: Neufeld et al. source for a heavy quark
AdS/CFT: Stress tables with /s=1/(4 )
R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)
pT = 3.14 GeV
BB et al., Phys. Lett. B 675, 340 (2009)
No Mach-like peaks:
AdS/CFT: Strong influence of the Neck region
Static medium and isochronous freeze-out needed for comparison
t=4.5/v fm
S. Gubser et al, Phys. Rev. Lett. 100, 012301 (2008)
BB et al., Phys. Lett. B 675, 340 (2009)
J. Noronha et al., Phys. Rev. Lett. 102, 102301 (2009)
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Expanding Medium I
Satarov et al, PLB 627:64 (2005)
• Consequences of expansion?
Transverse flow causes distortion
Expansion broadens Mach cone angle
• Predictions:
Radial flow, Elliptic flow
Mach cones are sensitive to the background flow
• Qualitative, model-independent effect
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Expanding Medium II
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)
• Two-particle correlation (Tfreeze-out < Tcrit = 130 MeV):
near-side jet
dE/dt = 1 GeV/fm
Jet 150
Etot = 5 GeV
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Expanding Medium IIIEtot = 5 GeV
broad away-side peak double peaked structure
due to non-central jets
pTtrig = 3.5 GeV
PHENIX, Phys. Rev. C 77, 011901 (2008)
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vjet =0.999
BB et al., arXiv: 1005.5461
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Expanding Medium IVEtot = 10 GeV
Strong impact of the Diffusion wake
broad away-side peak double peaked structure
Causes smaller dip for pT=2 GeV
pTtrig = 7.5 GeV
6 < pTtrigger < 10
1.5 < pTassoc < 2.5
STAR, arXiv: 1004.2377f
Yie
ld
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Expanding Medium V
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Comparing different deposition scenarios, one sees that
„cone“ angle approximately the same for different deposition scenarios
pTassoc = 2.0 GeV: No double-peaked structure for pure energy
deposition scenario due to thermal smearking
pTtrig = 3.5 GeV
pTassoc = 3.0 GeVpT
assoc = 2.0 GeV
vjet =0.999 BB et al., arXiv: 1005.5461
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Expanding Medium VI
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Conical emission angle also appears for subsonic jets Not a Mach cone
Considering a bottom quark (M=4.5 GeV), propagating at vjet < cs
(on-shell energy-momentum deposition scenario)
pTassoc = 2.0 GeV
Cu+Cu: Similar away-side shoulder width, double-peak structure reappars for pT
assoc = 3 GeV
BB et al., arXiv: 1005.5461 PHENIX, PRL98, 232302 (2007)
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MARTINI + MUSIC
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MARTINI: Modular Algorithm for Relativistic Treatment of Heavy
IoN Interactions
Incorporating an event-averaged MARTINI source term into the
(3+1)d hydro evolution MUSIC (MUScl – Monotonic Upstream CenteredStream [for conservaion laws] - for Ion Collisions)B. Schenke et al., Phys. Rev. C 80, 054913 (2009), B. Schenke et al., arXiv:1004.1408
B. Schenke, Talk at the RHIC & AGS Annual User’s Meeting, BNL, June 2010 Qualitative similar result
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Mach Cones in Transport Theorylocal energy density
“perturbative” scenario
momentum density
“pure energy” scenario
Diffusion wake
D. Molnar, AIP Conf. Proc. 1182 ,791 (2009)
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BAMPS
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BAMPS: Boltzmann Approach of MultiParton Scatterings
A transport algorithm solving the Boltzmann equations for on-shellpartons with pQCD interactions
C. Greiner, Talk at the Opening Symposium of the JET Collaboration, Berkeley, June 2010
Box scenario, no expansion, massless Boltzmann gas interactions, 2 -> 2
The shock front (Mach front) gets broader and vanish with more dissipation
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Jets in pQCD
R. Neufeld et al, Phys. Rev. C 78, 041901 (2008)
Considering a static medium and linearized hydrodynamicsfor a punch-though jet
1
s 4
=
3
s 4
=
6
s 4
=
R. Neufeld et al., Phys. Rev. C 79, 054909 (2009)
Signal dissolves with viscosity
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Jets in pQCD
R. Neufeld and T. Renk, arXiv:1001.5068.
Crescendo Deposition Scenario1 can lead to adouble-peaked structure, depending on l2
and /s
Deflection due to background flow and averaging matters and can lead to the double-peaked away-side structure dependingon cross-section H. Li et al., arXiv: 1006.2893.
Likewise, a jet shower can result in a double-peaked away-side
H. Li et al., arXiv: 1006.2893.
Static medium
1Increasing number of radiated gluons deposit energy Ep >> DEtot2local medium excitation parameter
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Hot Spots ICan fluctuating initial condition explain the 2+3-particle correlations?
Takahashi et al, PRL 103, 242301 (2009)
F. Grassi, Talk at the Glasma Workshop, BNL, May 2010
R. Andrade et al., arXiv: 0912.0803
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Hot Spots IICheck with one single hot spot
Can exp. data be corrected? Heavy quark jets are not affected
t=9.36 fmt=0 fm
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Full Jet Reconstruction
What happened to the Mach cone?
J. Putschke, Talk at RHIC and AGS Users Meeting 2009
Strong diffusion wake!
Flow profile at freeze-out after background subtraction
Jet 150
Test Proposal:Take a hydro-jet event, apply different jet reconstructionalgorithms and compare them
Jet 180
Summary Different source terms may lead to different structures on the away-side
(pQCD, AdS/CFT, …)
„Conical“ signal can be created:
by averaging over wakes created by jets in different events.
There is a deflection of particles emitted due to collectivetransverse flow.
Structure cannot directly be related to EoS, but is a measure for the flow
Quite insensitive to deposition mechanism, jet velocity (evenfor subsonic jets), and system size
Necessary to study heavy-flavor tagged jets.
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Measured away-side structure may be due to initial fluctuations
Mach cones have to occur in heavy-ion collisions if there is a fluid