Mach Cone Studies in (3+1)d Ideal Hydrodynamics
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Mach Cone Studies in (3+1)d Mach Cone Studies in (3+1)d Ideal HydrodynamicsIdeal Hydrodynamics
Barbara Betz,Barbara Betz,Philip Rau, Dirk Rischke, Horst Stöcker, Giorgio Philip Rau, Dirk Rischke, Horst Stöcker, Giorgio
TorrieriTorrieri
Institut für Theoretische PhysikInstitut für Theoretische PhysikJohann Wolfgang Goethe-UniversitätJohann Wolfgang Goethe-Universität
Frankfurt am MainFrankfurt am Main
LHC Workshop CERN, 31. 5. 2007LHC Workshop CERN, 31. 5. 2007
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ContentsContents
I.I. IntroductionIntroduction• Measured Two- and Three-Particle Measured Two- and Three-Particle
CorrelationsCorrelations
I.I. (3+1)d hydrodynamical approach (3+1)d hydrodynamical approach • Jet EvolutionJet Evolution• Two- and Three-Particle CorrelationsTwo- and Three-Particle Correlations
Different Energy and Momentum Different Energy and Momentum DepositionDeposition
15 GeV jet 15 GeV jet 30 GeV jet30 GeV jet 1500 particles total multiplicity1500 particles total multiplicity
I.I. ConclusionConclusion
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Two-Particle CorrelationTwo-Particle Correlation
F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006)
Sideward peaksSideward peaks
4 < p4 < pTTtrigtrig < 6 GeV/c < 6 GeV/c
0.15 < p0.15 < pTTassocassoc < 4 < 4
GeV/cGeV/c
• Peaks reflect interaction of jet with medium
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Three-Particle CorrelationThree-Particle Correlation
Au+Au central 0-12%
Δ2
Δ1
J. Ulery [STAR Collaboration],arXiv:0704.0224v1
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Hydrodynamical ApproachHydrodynamical Approach
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(3+1)d Ideal Hydrodynamik(3+1)d Ideal Hydrodynamik
Assume: Near-side jet not influenced by mediumAssume: Near-side jet not influenced by medium
Bag Model EoS with a 1Bag Model EoS with a 1stst order phase transition order phase transition
• Bjorken cylinderBjorken cylinder
• initial radius r = 3.5 fminitial radius r = 3.5 fm
• 00 = 1 fm/c = 1 fm/c
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Energy DepositionEnergy Deposition We compare:We compare:
15 GeV jet15 GeV jet 30 GeV jet30 GeV jet 1500 particles total multiplicity1500 particles total multiplicity
Jet deposits its energy and momentumJet deposits its energy and momentum
• within t = 1 fm/cwithin t = 1 fm/c• in equal time intervalsin equal time intervals
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Energy and Momentum Energy and Momentum DepositionDeposition
within t = 1 fm/cwithin t = 1 fm/c
of a 15 GeV jetof a 15 GeV jet
http://waterocket.explorer.free.fr/images/bullet1.jpghttp://waterocket.explorer.free.fr/images/bullet1.jpg
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Jet EvolutionJet Evolution
t = 6.4 fm/ct = 6.4 fm/cCreation of a bow shockCreation of a bow shock
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Momentum DistributionMomentum Distribution
t = 6.4 fm/ct = 6.4 fm/c
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Freeze-out• Stopped hydrodynamical evolution after t=6.4 fm/cStopped hydrodynamical evolution after t=6.4 fm/c
Isochronous freeze-outIsochronous freeze-out Cooper-Frye formulaCooper-Frye formula
• Considered a gas of Considered a gas of and and
• Using the Share programUsing the Share program
for a 50for a 5033 grid grid and 40 events and 40 events
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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
Energy and Momentum Deposition
in equal time intervals
of a 15 GeV jet
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Jet EvolutionJet Evolution
t = 6.4 fm/ct = 6.4 fm/cMach Cone like signalMach Cone like signal
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Momentum DistributionMomentum Distribution
t = 6.4 fm/ct = 6.4 fm/c
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Particle CorrelationsParticle Correlations
Mach Cone like signalMach Cone like signal
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Single and MultipleSingle and Multiple
Energy and Momentum DepositionEnergy and Momentum Deposition
of a 30 GeV jetof a 30 GeV jet
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Jet EvolutionJet Evolution
singlesingle multiplemultiple
bow shockbow shock
energy and momentum depositionenergy and momentum deposition
t = 6.4 fm/ct = 6.4 fm/c
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Momentum DistributionMomentum Distribution
singlesingle multiplemultipleenergy and momentum depositionenergy and momentum depositiont = 6.4 fm/ct = 6.4 fm/c
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Two-Particle CorrelationTwo-Particle Correlation
Jet SignalJet Signal
singlesingle multiplemultiple
energy and momentum depositionenergy and momentum deposition
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Three-Particle CorrelationThree-Particle Correlation
singlesingle multiplemultiple
energy and momentum depositionenergy and momentum deposition
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ConclusionConclusionI.I. Two- and Three-Particle CorrelationTwo- and Three-Particle Correlation
• Sideward peaks appear and reflectSideward peaks appear and reflect• interaction of jet with mediuminteraction of jet with medium
I.I. Hydrodynamical approach and Freeze-outHydrodynamical approach and Freeze-out
• Bag Model EoS Bag Model EoS • Bjorken-like expansionBjorken-like expansion
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 Jet EnergyJet Energy
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BackupBackup
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Jet QuenchingJet Quenching Suppression of the Suppression of the away-side jetsaway-side jets
in Au+Au collisionsin Au+Au collisions
4 < p4 < pTTtrigtrig < 6 GeV/c < 6 GeV/c
ppTTassocassoc > 2 GeV/c > 2 GeV/c
Compared to p+p Compared to p+p collisionscollisions
Jet QuenchingJet Quenching
J. Adams [STAR Collaboration], Phys. Rev. Lett. 91 072304 (2003)
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Freeze-out ResultsFreeze-out Results
Jet SignalJet Signal
Particles with pParticles with pxx enhanced enhanced
EEjetjet = 15 GeV = 15 GeV
depositiondeposition
singlesingle
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High Energy High Energy
Jet SignalJet Signal
EEjetjet = 30 GeV = 30 GeV
depositiondeposition
multiplemultiple
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Origin of Sideward PeaksOrigin of Sideward Peaks