Mach Cone Studies in (3 1)d Ideal Hydrodynamics

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Mach Cone Studies in (31)d Ideal Hydrodynamics

• Barbara Betz,
• Philip Rau, Dirk Rischke, Horst Stöcker, Giorgio
  Torrieri
• Institut für Theoretische Physik
• Johann Wolfgang Goethe-Universität
• Frankfurt am Main

LHC Workshop CERN, 31. 5. 2007
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Contents

• Introduction
• Measured Two- and Three-Particle Correlations
• (31)d hydrodynamical approach
• Jet Evolution
• Two- and Three-Particle Correlations
• Different Energy and Momentum Deposition
• 15 GeV jet
• 30 GeV jet
• 1500 particles total multiplicity
• Conclusion

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Two-Particle Correlation

• Sideward peaks
• 4 lt pTtrig lt 6 GeV/c
• 0.15 lt pTassoc lt 4 GeV/c

F. Wang STAR Collaboration, Nucl. Phys. A 774,
129 (2006)

• Peaks reflect interaction of jet with medium

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Three-Particle Correlation
AuAu central 0-12
Df1
??2
Df2
??1
J. Ulery STAR Collaboration, arXiv0704.0224v1
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Hydrodynamical Approach
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(31)d Ideal Hydrodynamik

• Assume Near-side jet not influenced by medium

• Bjorken cylinder

• initial radius r 3.5 fm

• t0 1 fm/c

• Bag Model EoS with a 1st order phase transition

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Energy Deposition

• We compare
• 15 GeV jet
• 30 GeV jet
• 1500 particles total multiplicity
• Jet deposits its energy and momentum
• within t 1 fm/c
• in equal time intervals

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Energy and Momentum Depositionwithin t 1
fm/cof a 15 GeV jet
http//waterocket.explorer.free.fr/images/bullet1.
jpg
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Jet Evolution
t 6.4 fm/c
Creation of a bow shock
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Momentum Distribution
t 6.4 fm/c
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Freeze-out

• Stopped hydrodynamical evolution after t6.4
  fm/c
• Isochronous freeze-out
• Cooper-Frye formula

• Considered a gas of p and r

• Using the Share program
• for a 503 grid
• and 40 events

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Particle Correlations

• Clear Jet Signal

• No Mach Cone

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Energy and Momentum Deposition in equal time
intervals of a 15 GeV jet
A. Filippone, www.aerodyn.org/Acoustics/Sound/soun
d.html
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Jet Evolution
t 6.4 fm/c
Mach Cone like signal
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Momentum Distribution
t 6.4 fm/c
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Particle Correlations

• Mach Cone like signal

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Single and MultipleEnergy and Momentum
Deposition of a 30 GeV jet
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Jet Evolution
multiple
single
energy and momentum deposition
t 6.4 fm/c
bow shock
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Momentum Distribution
single
multiple
energy and momentum deposition
t 6.4 fm/c
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Two-Particle Correlation
multiple
single
energy and momentum deposition

• Jet Signal

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Three-Particle Correlation
multiple
single
energy and momentum deposition
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Conclusion

• Two- and Three-Particle Correlation
• Sideward peaks appear and reflect
• interaction of jet with medium
• Hydrodynamical approach and Freeze-out
• Bag Model EoS
• Bjorken-like expansion
• Jet visible independent of nature of energy
  deposition
• Evolution of a Mach Cone depends on
• Energy and Momentum deposition
• Jet Energy

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Backup
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Jet Quenching

• Suppression of the
• away-side jets
• in AuAu collisions
• 4 lt pTtrig lt 6 GeV/c
• pTassoc gt 2 GeV/c
• Compared to pp collisions

J. Adams STAR Collaboration, Phys. Rev. Lett.
91 072304 (2003)
Jet Quenching
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Freeze-out Results
single
deposition
Ejet 15 GeV

• Jet Signal

• Particles with px enhanced

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High Energy
multiple
deposition
Ejet 30 GeV

• Jet Signal

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Origin of Sideward Peaks