Mach Cones in a Perturbative Quark-Gluon Plasma

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Mach Conesin a Perturbative Quark-Gluon Plasma

• Berndt Mueller Duke University
• Quark Matter 2008
• Jaipur, India, 2 - 10 February 2008

Credits to M. Asakawa R.B. Neufeld C. Nonaka
J. Ruppert
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An interesting question

• Is a Mach cone created when a supersonic parton
  propagates through the quark gluon plasma?
• A Mach cone is formed when an object moves faster
  than the speed of sound in the medium.
• What is the energy and momentum perturbation of
  the medium due to a fast parton?

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In real life.
Relevant dynamical quantities
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Formalism
Calculate the interaction of the color field of
the supersonic parton with the medium by means of
semi-classical transport theory
If the medium is color neutral, to lowest order
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Hydrodynamics
In the macrocopic limit this yields hydrodynamic
equations with source terms
Momentum space integrals yield term mD2
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Unscreened source
For an unscreened color charge, analytical result
in u?1 limit
Applying infrared (screening) and ultraviolet
(quantum) cuts on the ?-integral gives the
standard expression for collisional energy loss
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With screening
Use HTL di-electric functions for ? ukz
Expressions for J?(x) can be reduced to sums of
products of two-dimensional Fourier integrals,
which can be performed numerically after contour
rotation in the complex plane.
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Energy density
J0(?,z) screened
J0(?,z) unscreened
(GeV)4
(GeV)4
? ?
? ?
(z - ut) ?
(z - ut) ?
u 0.99
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z-Momentum density
Jz(?,z) screened
Jz(?,z) unscreened
(GeV)4
(GeV)4
? ?
? ?
(z - ut) ?
(z - ut) ?
u 0.99
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x-Momentum density
Jx(?,z) screened
Jx(?,z) unscreened
(GeV)4
(GeV)4
? ?
? ?
(z - ut) ?
(z - ut) ?
u 0.99
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More comparisons
u 0.99
(GeV)4
(GeV)4
Jz(z-ut) at ? 2 GeV-1
Jx(z-ut) at ? 1 GeV-1
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Linearized hydro
Linearize hydro eqs. for a weak source T00 ? ??
??, T0i ? gi .
Solve in Fourier space for longitudinal sound
and dissipative transverse perturbation
See J. Casalderrey-Solana, E.V. Shuryak and D.
Teaney, arXivhep-ph/0602183
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The Mach cone (at last!)
Unscreened source with ?min/max cutoff
Energy density
Momentum density
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Contour plots
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pQCD vs. N4 SYM
u 0.99955 c
R.B. Neufeld (preliminary)
Chesler Yaffe arXiv0712.0050
u 0.75 c
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Conclusion
Summary We have calculated the energy and
momentum density deposited into a perturbative,
thermal QCD plasma by the color field of a fast
moving parton. When treated as a source in
linearized dissipative hydrodynamics, the
perturbation induces a sonar Mach cone and a
diffusive wake. Apart from logarithmic effects,
the effect has a well defined relativistic
limit. The emerging picture closely resembles
that found in the N 4 super-symmetric gauge
theory at strong coupling. An attempt to explore
the effects of the (screened) source term in a 3D
relativistic, ideal hydro code in progress.