Sonic Mach Cones in a Perturbative QuarkGluon Plasma

1
Sonic Mach Cones in a Perturbative Quark-Gluon
Plasma
Presented by Bryon Neufeld (of Duke University)
on August 23rd 2008 In collaboration with Berndt
Mueller and Joerg Ruppert
1 arXiv0802.2254, 2 arXiv0805.0385, 3
arXiv0807.2996
2
Jets as a Probe of the QGP
Formed when two energetic partons scatter at a
large angle and acquire a large transverse
momentum relative to the beam direction

• Thanks to J. Casalderrey-Solana

3

• 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.

4
Why so much interest?
Possibilities Deflected Jets, Large Angle
Gluon Radiation, Cherenkov, Mach cone shock waves
Au-Au at 200 GeV c.m. energy di-hadron
correlations Per-trigger yield distribution
PHENIX
5
Start with the Question What is the energy and
momentum perturbation of a QGP due to a fast
parton?
Treat the fast parton as the source of an
external color field interacting with a QGP and
described by the distribution f(x,p,Q). The
Vlasov equation for this system is
6

• Using Wongs Chromomagnetic Equations of Motion

Take moments in Q space
7
Yields the basic equations needed
f1 vanishes in equilibrium (color neutral),
truncate the series at order gA
To finally get
8
Taking the microscopic to the macroscopic
With assumption of local therm. Eq., yields
9
Back to the Question What is the energy and
momentum perturbation of a QGP due to a fast
parton?In this approach the answer is

• J gives the energy/momentum deposited per unit
  time, it is a source term
• Assumptions the medium is perturbative in
  coupling g, hydrodynamics

10
The source term has been explicitly evaluated
both with and without medium screening included.
Linearized hydro
arXiv0805.0385

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

11
Results deposited energy density
-4 fm
12
Results deposited momentum density
-4 fm
13
Turning the Hydrodynamic Solution into a Particle
Spectrum
Use a Cooper Frye Freeze-Out Prescription (choose
the minimal viscosity solution)?
Compare the spectrum for two different freeze-out
scenarios. Examine sensitivity of result to
freeze-out assumption. Remove the diffusive
contribution for clarity.
14
Two different Freeze-Out Scenarios
Radial Scenario
Phi 0
5 fm rad.
Freeze-Out Surface
Isochronous Brick
Infinite Freeze-Out Volume at fixed time
15
Results
Radial Scenario
Isochronous Brick
Near side distribution Added by Hand Using Simple
Ansatz
16
Summary

• There is experimental evidence that sonic Mach
  cones are induced by fast partons at RHIC
• A theoretical investigation into the formation of
  Mach cones in the QGP should first start with the
  more general question What is the distribution
  of energy and momentum deposited into a QGP due
  to a fast parton?
• This distribution is calculated in a pQGP and we
  find a mach cone in the linearized hydrodynamics.
  
• With CERTAIN ASSUMPTIONS, one can obtain a
  particle spectrum that has a similar structure as
  that seen at RHICHowever, take this with a big
  grain of salt!
• Any meaningful comparison with data requires
  incorporating a realistic source term in an
  expanding medium

17
Backup Slides