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Investigations on Jet Evolution in Investigations on Jet Evolution in
(3+1)d Ideal Hydrodynamics(3+1)d Ideal HydrodynamicsBarbara Betz,Barbara Betz,
Dirk Rischke, Horst Stöcker, Giorgio TorrieriDirk Rischke, Horst Stöcker, Giorgio Torrieri
Institut für Theoretische PhysikInstitut für Theoretische PhysikJohann Wolfgang Goethe-UniversitätJohann Wolfgang Goethe-Universität
Frankfurt am MainFrankfurt am Main
H-QM Graduate Days, 18. 07. 2007H-QM Graduate Days, 18. 07. 2007
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ContentsContents
I.I. Introduction and MotivationIntroduction and Motivation• Measured Jet Signals in Heavy-Ion CollisionsMeasured Jet Signals in Heavy-Ion Collisions
II.II. (3+1)d hydrodynamical approach (3+1)d hydrodynamical approach • Jet Implementation Jet Implementation • Jet EvolutionJet Evolution• Two- and Three-Particle CorrelationsTwo- and Three-Particle Correlations
Different Energy and Momentum Different Energy and Momentum DepositionDeposition
III.III. Conclusion and OutlookConclusion and Outlook
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The QCD Phase DiagramThe QCD Phase Diagram
John von Neumann-Institut for Computing, Forschungszentrum-Jülich
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Jet QuenchingJet Quenching Suppression of the Suppression of the
away-side jetsaway-side jets
ppTTassocassoc > 2 GeV/c > 2 GeV/c
Signal for QGPSignal for QGP
J. Adams [STAR Collaboration], Phys. Rev. Lett. 91 072304 (2003)
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Two-Particle CorrelationTwo-Particle Correlation
F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006)
Sideward peaksSideward peaks
0.15 < p0.15 < pTTassocassoc < 4 GeV/c < 4 GeV/c
• Peaks reflect interaction of jet with mediumPeaks reflect interaction of jet with medium
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Origin of Sideward PeaksOrigin of Sideward Peaks
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Three-Particle CorrelationThree-Particle Correlation
Au+Au central
Δ2
Δ1
J. Ulery [STAR Collaboration],arXiv:0704.0224v1
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Hydrodynamical ApproachHydrodynamical Approach
understand theoretically the process of the jet-understand theoretically the process of the jet-medium interactionmedium interaction
QGP behaves like a fluidQGP behaves like a fluid can be described using ideal hydrodynamicscan be described using ideal hydrodynamics
AssumptionsAssumptions
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(3+1)d Ideal Hydrodynamik(3+1)d Ideal Hydrodynamik Hydrodynamics represents (local) conservation ofHydrodynamics represents (local) conservation of
EoSEoS
• energy-momentumenergy-momentum
• (local) charge(local) charge
If matter is in local thermodynamical equilibriumIf matter is in local thermodynamical equilibrium
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Deposition ScenariosDeposition Scenarios We compare jets that deposit their energy (and We compare jets that deposit their energy (and
momentum)momentum)
• within t = 0.5 fm/cwithin t = 0.5 fm/c
• in equal time intervalsin equal time intervals
Solving: Solving:
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(3+1)d Hydrodynamik(3+1)d Hydrodynamik
• AssumeAssume: Near-side jet not influenced by medium: Near-side jet not influenced by medium
Ideal Gas/ Bag Model Ideal Gas/ Bag Model EoSEoS
• Implement a jet that ...Implement a jet that ...
moves with ~ cmoves with ~ c
Use the Frankfurt (3+1)d ideal Use the Frankfurt (3+1)d ideal hydrodynamical codehydrodynamical code
• Define a backgroundDefine a background
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Freeze-outFreeze-out• Stopped hydrodynamical evolution after a certain timeStopped hydrodynamical evolution after a certain time
Isochronous freeze-outIsochronous freeze-out Cooper-Frye formulaCooper-Frye formula
• Considered a gas of Considered a gas of , , andand
• Using the Share program (Monte Carlo)Using the Share program (Monte Carlo)
for a proper number of events statistics for a proper number of events statistics
• Calculate two- and three-particle correlationsCalculate two- and three-particle correlations
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Jet DepositionJet Deposition
within t = 0.5 fm/cwithin t = 0.5 fm/c
into an into an expanding sphereexpanding sphere
http://waterocket.explorer.free.fr/images/bullet1.jpghttp://waterocket.explorer.free.fr/images/bullet1.jpg
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Jet EvolutionJet Evolution
t = 11.52 fm/ct = 11.52 fm/cCreation of a bow shockCreation of a bow shock
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Particle CorrelationsParticle Correlations
Clear Jet SignalClear Jet Signal No Mach ConeNo Mach Cone
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A. Filippone, www.aerodyn.org/Acoustics/Sound/sound.html
Jet DepositionJet Deposition
in in equal time intervalsequal time intervals
into a homogeneous into a homogeneous backgroundbackground
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Jet EvolutionJet Evolution
Mach Cone like signalMach Cone like signal t = 6.4 fm/ct = 6.4 fm/c
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Single and MultipleSingle and Multiple
Energy and Momentum DepositionEnergy and Momentum Deposition
of a 15 GeV jetof a 15 GeV jet
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Jet EvolutionJet Evolution
singlesingle multiplemultiple
energy and momentum depositionenergy and momentum deposition
t = 6.4 fm/ct = 6.4 fm/c
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Two-Particle CorrelationsTwo-Particle Correlations
Jet SignalJet Signal
singlesingle multiplemultiple
energy and momentum depositionenergy and momentum deposition
Mach Cone like signalMach Cone like signal
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Three-Particle CorrelationsThree-Particle Correlations
singlesingle multiplemultiple
energy and momentum depositionenergy and momentum deposition
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ConclusionConclusion
I.I. Jets serve as a probe for the QGPJets serve as a probe for the QGP• Study theoretically the jet-medium Study theoretically the jet-medium
interactioninteraction
II.II. Hydrodynamical approach and Freeze-outHydrodynamical approach and Freeze-out
• Ideal Gas/ Bag Model EoS Ideal Gas/ Bag Model EoS Jet visible independent of nature of energy Jet visible independent of nature of energy
depositiondeposition Evolution of a Mach Cone depends onEvolution of a Mach Cone depends on
Energy and Momentum depositionEnergy and Momentum deposition
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OutlookOutlook
Determine a physical background and Determine a physical background and source termsource term pQCDpQCD
Calculate the respective jet evolutionCalculate the respective jet evolution
Performing the freeze-out by solving the Performing the freeze-out by solving the Cooper-Frye formula Cooper-Frye formula
Thank you for your Thank you for your attention !attention !