Conical Flow induced by Quenched QCD Jets

1
Conical Flow induced by Quenched QCD Jets
Jorge Casalderrey-Solana, Edward Shuryak and
Derek Teaney, hep-ph/0411315
SUNY Stony Brook
2
Outline

• Basic Ingredients
• Hydrodynamics
• Thermalization of energy loss
• Assumption small perturbations due to energy
  loss
• Solution to the linearized problem
• Conical shock waves
• Possible experimental confirmation
• Conclusions.

3
Hydrodynamics

• (local) Energy-momentum and baryon number
  conservation.
• At mid rapidity (neglecting nB)
• Ideal case (h0) provides a remarkable
  description of radial and elliptic flows at RHIC
• The viscosity at RHIC seems to be close to its
  minimal conjectured bound.

4
Jet Quenching and Energy Loss

• High pt particles lose energy in the medium
• Radiative losses (main effect)
• Collision losses
• Ionization losses
• (bound states)
• From the hydrodynamical point of view, the
  different mechanisms may be only distinguished by
  the deposition process (what mode they excite)
• We study this modification through hydrodynamics.
• Similar ideas have been discussed by H. Stoeker
  (nucl-th/0406018)

?
ShuryakZahed, hep-ph/0406100
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Basic Assumptions

• The deposited energy thermalizes at a scale
• Minimal value gtgt
  point-like . Gs will be the only scale of the
  source
• Outside of the source, the modification of the
  properties of the medium is small
• Thus, linearized hydrodynamic description is
  valid

ltlt
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Summing the Spherical Waves
Particle moving in the static medium with
velocity v
After the disturbance is thermalized
Given the symmetries of the problem, we need to
specify
The different terms lead to different excitations
of the medium
Adding all displacements we obtain the Mach cone
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Two (linear) Hydro Modes
After Fourier transformed (space coordinates)
By defining the system
decouples
Sound waves (propagating)
Diffuson (not propagating)
Excitations
Sound
Diffuson
?
Yes
No
Yes
Yes
No
Yes
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Flow Picture
Diffuson Matter moving mainly along the jet
direction
Sound motion along Mach direction.
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Considerations about Expansion

• c2s is not constant though system evolution
  csQGP , cs in the resonance gas
  and cs0 in the mixed phase.

(Hung,E. Shuryak hep-ph/9709264)

• Distance traveled by sound is reduced ?Mach
  direction changes

lt RHIC

• q 1.23 rad 71o

p/e(e) EoS along fixed nB/s lines

• Flow of the background medium modifies the shape
  and angle of the cone (Satarov et al.)

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Spectrum

• Cooper-Fry with equal time freeze out

• At low ptTf

• Pt gtgtthe spectrum is more sensitive to the
  hottest points (shock and regions close to the
  jet)
• If the jet energy is enough to punch through, ?
  fragmentation part on top of thermal spectrum

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Two Particle Correlations
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Is such a sonic boom already observed?
?? /-1.231.91,4.37
STAR Preliminary
(1/Ntrig)dN/d(Df)
M.Miller, QM04
Flow of matter normal to the Mach cone seems to
be observed!
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Conclusions

• We have used hydrodynamics to follow the energy
  deposited in the medium.
• Finite cs leads to the appearance of a Mach cone
  (conical flow correlated to the jet)
• Depending on the initial conditions,the direction
  of the cone is reflected in the final particle
  production.

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Outlook
Problems that need to be addressed (on progress)

• Systematic study of initial conditions
• Role of non-linearities (mixing the modes)
• Precise effect of changing speed of sound as well
  as the expanding media
• Realistic simulation of collision geometry
• Three particle correlations.

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Swinging the back jet
Assume a boost invariant medium and a
yj-distribution for the backjet P(yj) (flat).
Boosting by yj we assume a particle distribution
q
p
After boosting back to the lab frame
Now we integrate over yj
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Swinging the back jet (II)
x
If we simply rotate the jet axis (Vitev)
d
q
q
z
y
And use
Integrating over q
However long tails may fill up the cone.
I. Vitev hep-ph/0501255
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How to observe it?

• the direction of the flow is normal to the Mach
  cone, defined entirely by the ratio of the speed
  of sound to the speed of light
• Unlike the (QCD) radiation, the angle is not
  shrinking (1/?) with the increase of the momentum
  of the jet but is the same for all jet momenta
• At high enough pt a punch through is expected,
  filling the cone