Heavy Quark Propagation in an AdS/CFT plasma

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Heavy Quark Propagation in an AdS/CFT plasma

• Jorge Casalderrey-Solana
• LBNL

Work in collaboration with Derek Teaney
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Outline
Langevin dynamics for heavy quarks
Calibration of the noise
Broadening from Wilson Lines
AdS/CFT computation
Broadening at finite velocity
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Langevin Dynamics
Heavy Quark MgtgtT ? moves slowly
de Broglie w. l.
HQ is classical
Random (white) noise
Einstein relations
Medium properties
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Heavy Quarks at RHIC
The Langevin model to is used to describe charm
and bottom quarks
Fits to data allow to extract the diffusion
coefficient
(Moore Teaney, van Hees Rapp)
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How to Calibrate the Noise
In perturbation theory
But we cannot use diagrams!
MgtgtT ? long deflection time
?
Thermal average
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Broadening from Wilson Lines
E(t1,y1)Dt1dy1
E(t2,y2)Dt2dy2
Small fluctuation of the HQ path
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AdS/CFT computation
Static Quark straight string stretching to the
horizon
v0
ue
We solve the small fluctuation problem (mechanica
l problem)
u01
Horizon
In terms of the classical solution
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Broadening and Diffusion in AdS/CFT
In perturbation theory
Depends explicitly on Nc. Different from h/s
It is not universal!
Putting numbers
To compare with QCD gt rescale the degrees of
freedom
(Liu, Rajagopal, Wiedemann)
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Probe at finite velocity
t
Trailing string gt work over tension
xvt
x
same k!
Drag valid for all p !
(Herzog, Karch, Kovtun, Kozcaz and Yaffe
Gubser)
Broadening gt repeat fluctuation problem
Depends on the energy of the probe!
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Conclusions
We have provided a non-perturbative definition
of the momentum broadening as derivatives of a
Wilson Line
This definition is suited to compute k in N4 SYM
by means of the AdS/CFT correspondence.
The calculated k scales as and takes much
larger values than the perturbative extrapolation
for QCD.
The results agree, via the Einstein relations,
with the computations of the drag coefficient.
This can be considered as an explicit check that
AdS/CFT satisfy the fluctuation dissipation
theorem.
The momentum broadening k at finite v diverges as
.
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Back up Slides
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Computation of (Radiative Energy Loss)
(Liu, Rajagopal, Wiedemann)
Dipole amplitude two parallel Wilson lines
in the light cone
Order of limits
String action becomes imaginary for
For small transverse distance
entropy scaling
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Energy Dependence of
(JC X. N. Wang)
From the unintegrated PDF
Evolution leads to growth of the gluon density,
In the DLA
HTL provide the initial conditions for evolution.
Saturation effects ?
For an infinite conformal plasma (LgtLc) with
Q2max6ET.
At strong coupling
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Noise from Microscopic Theory
HQ momentum relaxation time
Consider times such that

microscopic force (random)
?
charge density
electric field
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Heavy Quark Partition Function
McLerran, Svetitsky (82)
YM states
YM Heavy Quark states
Integrating out the heavy quark
Polyakov Loop
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Heavy Quark Partition Function
McLerran, Svetitsky (82)
YM states
YM Heavy Quark states
Integrating out the heavy quark
Polyakov Loop
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k as a Retarded Correlator
k is defined as an unordered correlator
From ZHQ the only unordered correlator is
Defining
In the w?0 limit the contour dependence
disappears
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Force Correlators from Wilson Lines
Integrating the Heavy Quark propagator
Which is obtained from small fluctuations of the
Wilson line
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Momentum Distribution
-T/2
T/2
v
f0 (b)
ff (b)