Investigations on Jet Evolution in (3+1)d Ideal Hydrodynamics Barbara Betz, Dirk Rischke, Horst...

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

Graduate Days, 18. 07. 2007 Graduate Days, 18. 07. 2007

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


The QCD Phase DiagramThe QCD Phase Diagram

John von Neumann-Institut for Computing, Forschungszentrum-Jülich


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)


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


Origin of Sideward PeaksOrigin of Sideward Peaks


Three-Particle CorrelationThree-Particle Correlation

Au+Au central

Δ2

Δ1

J. Ulery [STAR Collaboration],arXiv:0704.0224v1


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


(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


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:


(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


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


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


Jet EvolutionJet Evolution

t = 11.52 fm/ct = 11.52 fm/cCreation of a bow shockCreation of a bow shock


Particle CorrelationsParticle Correlations

Clear Jet SignalClear Jet Signal No Mach ConeNo Mach Cone


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



Mach Cone like signalMach Cone like signal t = 6.4 fm/ct = 6.4 fm/c


Single and MultipleSingle and Multiple

Energy and Momentum DepositionEnergy and Momentum Deposition

of a 15 GeV jetof a 15 GeV jet



singlesingle multiplemultiple

energy and momentum depositionenergy and momentum deposition

t = 6.4 fm/ct = 6.4 fm/c


Two-Particle CorrelationsTwo-Particle Correlations

Jet SignalJet Signal



Mach Cone like signalMach Cone like signal


Three-Particle CorrelationsThree-Particle Correlations




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


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 !

Investigations on Jet Evolution in (3+1)d Ideal Hydrodynamics Barbara Betz, Dirk Rischke, Horst...

Documents

Transcript of Investigations on Jet Evolution in (3+1)d Ideal Hydrodynamics Barbara Betz, Dirk Rischke, Horst...