The Response of a

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The Response of a Thermal Quark-Gluon Plasma
to Radiating Hard Probes
Presented by Bryon Neufeld (of Duke
University)? Special thanks to my advisor Berndt
Muller arXiv nucl-th/0902.2950
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• Interesting Questions
• What is the energy and momentum perturbation of a
  QGP due to a fast parton?
• Similarly, Is a Mach cone created by a supersonic
  parton propagating through the quark gluon
  plasma?

• A Mach cone is formed when an object moves faster
  than the speed of sound relative to it's medium.

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Why so much interest?
Possibilities Deflected Jets Large Angle Gluon
Radiation Cerenkov Mach cone shock waves
Au-Au at 200 GeV c.m. energy di-hadron
correlations Per-trigger yield distribution
PHENIX
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A Theoretical Investigation What is the energy
and momentum perturbation of a QGP due to a fast
parton?
In Phys Rev C 78, 041901 (2008), Neufeld et al
presented formalism to derive energy/momentum
perturbation in kinetic theory?
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For an unscreened color charge obtain analytic
result Phys Rev D 78, 085015 (2008)?
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The source term has been explicitly evaluated
both with and without medium screening included,
now can examine medium response.
Linearized hydro

• These equations are valid in the limit of a weak
  source
• Solve for deposited energy density, sound
  momentum, and diffusion momentum
• Parameters

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RESULTS (Phys Rev C 78, 041901 (2008)? and Phys
Rev C (Submitted, 2008) arXivnucl-th/0807.2996)
?
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What Is Missing?

• Contribution of radiative energy loss to the
  medium response

The Phenomenology of Jet-Medium Interactions
Collisional
Radiative
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What is the energy deposited into the medium
per unit length by the fast parton due to
radiation?
The radiative energy loss of the parton
contributes to the medium excitation because
energetic radiated gluons act as an additional
source of collisional energy loss in the medium
after decoherence from original parton
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In order to calculate energy deposition, we must
determine radiation spectrum in medium
At each step, the spectrum gains new gluons, and
is depleted by energy loss
Require conservation of number emitted, and take
continuum form
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Can solve for f(?,?) numerically, take emission
spectrum Salgado and Wiedemann Phys Rev D 68,
014008 (2003)?
And qhat from Baier and Mehtar-Tani Phys Rev C
78, 064906 (2008)?
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Numerical Results for
Differential energy absorbed by medium lags
behind that emitted
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Determining the medium response via hydrodynamics
Consider back to back partons created at t 0
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Energy density wave excited at t 8 fm
Cylindrically Symmetric Results Presented in X
Plane for eta/s 0.2
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Energy density wave in GeV/fm3
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Magnitude of momentum density wave in GeV/fm3
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Turning the Hydrodynamic Solution into a Particle
Spectrum
Use a Cooper Frye Freeze-Out Prescription (choose
the minimal viscosity solution)?
Freeze-Out Scenario
Phi 0
Radial Scenario background velocity added by hand
12 fm rad.
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Near side distribution Added by Hand Using Simple
Ansatz
From peaks, cs 0.62, in calc., Cs 0.57
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Summary

• Investigated medium response to fast parton by
  calculating hydrodynamic source term from kinetic
  theory
• Added contribution from radiation by calculating
  spectrum of radiation in medium, which was used
  to find energy deposited per unit length
• Result for energy density wave generated from
  both radiative and collisional loss shown
• Showed animated dynamics of wave in medium
• CF freeze-out scenario with background radial
  flow, added by hand, can show double peak
  structure, however, need more rigorous scenario