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Mach Cone Studies with 3D Mach Cone Studies with 3D HydrodynamicsHydrodynamics
Barbara BetzBarbara Betz
Institut für Theoretische PhysikInstitut für Theoretische PhysikJohann Wolfgang Goethe-UniversitätJohann Wolfgang Goethe-Universität
Frankfurt am MainFrankfurt am Main
NCRH2007 Frankfurt, 18. April 2007NCRH2007 Frankfurt, 18. April 2007
ContentsContents
I.I. IntroductionIntroduction• Jet QuenchingJet Quenching• Two and Three-Particle CorrelationTwo and Three-Particle Correlation
I.I. (3+1)d hydrodynamical approach(3+1)d hydrodynamical approach• Jet ImplementationJet Implementation• Jet EvolutionsJet Evolutions• Freeze-outFreeze-out
I.I. ConclusionConclusion
Jet PropagationJet Propagation
F. Wang, QM06
Jet QuenchingJet Quenching Suppression of the Suppression of the
away-side jetsaway-side jets
in Au+Au collisionsin Au+Au collisions
4 < p4 < pTT < 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)
Two-Particle CorrelationTwo-Particle Correlation• Redistribution of energy to low pRedistribution of energy to low pTT-particles:-particles:
F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006)
Sideward peaksSideward peaks
4 < p4 < pTT < 6 GeV/c < 6 GeV/c
0.15 < p0.15 < pTTassocassoc < 4 < 4
GeV/cGeV/c
• Peaks reflect interaction of jet with medium
Origin of Sideward PeaksOrigin of Sideward Peaks
Three-Particle CorrelationThree-Particle Correlation
Au+Au central 0-12%
Δ2
Δ1
J. Ulery [STAR Collaboration],arXiv:0704.0224v1
Hydrodynamical ApproachHydrodynamical Approach
(3+1)d Hydrodynamik(3+1)d Hydrodynamik• Assume: Near-side jet not influenced by mediumAssume: Near-side jet not influenced by medium
Ideal Gas EoSIdeal Gas EoS
• Implement a jet that ...Implement a jet that ...
deposits energy deposits energy and and momentum within momentum within 0.5 fm/c0.5 fm/c
in a spherically in a spherically expanding expanding mediummedium
Use the Frankfurt (3+1)d ideal Use the Frankfurt (3+1)d ideal hydrodynamical codehydrodynamical code
Ideal Gas EoSIdeal Gas EoS
t = 11.52 fm/ct = 11.52 fm/c
Creation of a bow shockCreation of a bow shock
Freeze-outFreeze-out
Giorgio Giorgio TorrieriTorrieri
Freeze-out
• Stopped hydrodynamical evolution after t=11.52 fm/cStopped hydrodynamical evolution after t=11.52 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 10 events and 10 events
Freeze-out ResultsFreeze-out Results
Jet SignalJet Signal
More particles are producedMore particles are produced Particles with pParticles with pxx enhanced enhanced
Two-Particle CorrelationTwo-Particle Correlation
Clear Jet SignalClear Jet Signal No Mach ConeNo Mach Cone
Three-Particle CorrelationThree-Particle Correlation
Medium without jetMedium without jet Medium with jetMedium with jet
Rectangular Nucleus Rectangular Nucleus ApproachApproach
Ideal Gas EoSIdeal Gas EoS
• Implement a jet that ...Implement a jet that ...
deposits energy and deposits energy and momentum within momentum within 1 fm/c1 fm/c
into a static, into a static, homogeneous homogeneous mediummedium
VorticesVortices
• Jet SignalJet Signal
Smoke RingsSmoke Rings
t = 11.52 fm/ct = 11.52 fm/c
Discontinuous Energy LossDiscontinuous Energy Loss
Ideal Gas EoSIdeal Gas EoS
• Implement a jet that ...Implement a jet that ...
deposits energy of deposits energy of 2 GeV 2 GeV
in equal time in equal time intervals intervals ofoft = 1.6 fm/ct = 1.6 fm/c
into a static,into a static, homogeneous homogeneous mediummedium
Discontinuous Energy LossDiscontinuous Energy Loss
t = 7.2 fm/ct = 7.2 fm/c
Clear Jet SignalClear Jet Signal Clear Mach Cone SignalClear Mach Cone Signal
ConclusionConclusionI.I. Two- and Three-Particle Two- and Three-Particle
CorrelationCorrelation• Sideward peaks appear and reflectSideward peaks appear and reflect
• interaction of jet with medium andinteraction of jet with medium and• emission angle of Mach Coneemission angle of Mach Cone
I.I. Hydrodynamical approach Hydrodynamical approach with Freeze-outwith Freeze-out
• Ideal Gas EoS Ideal Gas EoS • Jet visible independent of nature of Jet visible independent of nature of
energy depositionenergy deposition• Clear Mach Cone appears in case Clear Mach Cone appears in case
of discontinous energy deposition of discontinous energy deposition
Open ProblemsOpen Problems
I.I. Influence of the backgroundInfluence of the background
I.I. Evolution of a fast projectileEvolution of a fast projectile
I.I. Freeze-out for “rectangular Freeze-out for “rectangular nucleus approach”nucleus approach”
BackupBackup
SHASTASHASTA• Solves finite difference versions ofSolves finite difference versions of
• via the method of time-step splitting (operator via the method of time-step splitting (operator splitting)splitting) sequentially solvingsequentially solving
Three-Particle CorrelationThree-Particle Correlation
F. Wang [STAR Collaboration], Nucl. Phys. A 774, 129 (2006)
11 = = ±±
==±±
=={{ 00±±22
J. Ulery [STAR Collaboration],arXiv:0704.0224v1
Mach Cone Speed of SoundMach Cone Speed of Sound
F. Wang, QM06
Emission Angle of the Mach ConesEmission Angle of the Mach Cones
cos θ =cs
vjet
~ 60 – 90°
massless QGP: cmassless QGP: css ~ 0.57 ~ 0.57 θ = 1.0 radθ = 1.0 rad
hadronic matter: chadronic matter: css ~ 0.3 ~ 0.3
11stst order phase transition: c order phase transition: css ~ 0 ~ 0
θ = 1.3 radθ = 1.3 rad
θ = 1.5 radθ = 1.5 rad
• vjet depends on the mass of the leading quarks
Break-up of the Mach ConeBreak-up of the Mach Cone
t = 7.2 fm/ct = 7.2 fm/c
Energy DistributionEnergy Distribution
Jet correlations in Jet correlations in p+p collisions:p+p collisions:
Back-to-back Back-to-back peaks appear.peaks appear.
Energy DistributionEnergy Distribution
Jet correlations in Jet correlations in central Au+Au central Au+Au collisions:collisions:
Away-side jet Away-side jet disappears for disappears for particles with pparticles with ptt > > 2 GeV/c 2 GeV/c
Energy DistributionEnergy Distribution
Jet correlations in Jet correlations in central Au+Au central Au+Au collisions:collisions:
Away-side jet Away-side jet (re)appears for (re)appears for particles with pparticles with pTT > > 0.15 GeV/c.0.15 GeV/c.