Mach Cone Studies in (3+1)d Ideal Hydrodynamics Barbara Betz, Philip Rau, Dirk Rischke, Horst...

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

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

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

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 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

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

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

Jet EvolutionJet Evolution

t = 6.4 fm/ct = 6.4 fm/cCreation of a bow shockCreation of a bow shock

Momentum DistributionMomentum Distribution

t = 6.4 fm/ct = 6.4 fm/c

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

Particle CorrelationsParticle Correlations

Clear Jet SignalClear Jet Signal No Mach ConeNo Mach Cone

A. Filippone, www.aerodyn.org/Acoustics/Sound/sound.html

Energy and Momentum Deposition

in equal time intervals

of a 15 GeV jet


t = 6.4 fm/ct = 6.4 fm/cMach Cone like signalMach Cone like signal


t = 6.4 fm/ct = 6.4 fm/c

Particle CorrelationsParticle Correlations

Mach Cone like signalMach Cone like signal

Single and MultipleSingle and Multiple

Energy and Momentum DepositionEnergy and Momentum Deposition

of a 30 GeV jetof a 30 GeV jet


singlesingle multiplemultiple

bow shockbow shock

energy and momentum depositionenergy and momentum deposition

t = 6.4 fm/ct = 6.4 fm/c


singlesingle multiplemultipleenergy and momentum depositionenergy and momentum depositiont = 6.4 fm/ct = 6.4 fm/c

Two-Particle CorrelationTwo-Particle Correlation

Jet SignalJet Signal



Three-Particle CorrelationThree-Particle Correlation



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

BackupBackup

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)

Freeze-out ResultsFreeze-out Results


Particles with pParticles with pxx enhanced enhanced

EEjetjet = 15 GeV = 15 GeV

depositiondeposition

singlesingle

High Energy High Energy


EEjetjet = 30 GeV = 30 GeV

depositiondeposition

multiplemultiple

Origin of Sideward PeaksOrigin of Sideward Peaks

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