Mach Cone Studies with 3D Hydrodynamics Barbara Betz Institut für Theoretische Physik Johann Wolfgang Goethe-Universität Frankfurt am Main NCRH2007 Frankfurt,

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.