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. 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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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


Outline

Langevin dynamics for heavy quarks

Calibration of the noise

Broadening from Wilson Lines

AdS/CFT computation

Broadening at finite velocity


Langevin Dynamics

Heavy Quark M>>T  moves slowly

de Broglie w. l.

HQ is classical

Random (white) noise

Einstein relations

Medium properties


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)


How to Calibrate the Noise

In perturbation theory

But we cannot use diagrams!

M>>T  long deflection time

Thermal average


Broadening from Wilson Lines

E(t1,y1)Dt1dy1

E(t2,y2)Dt2dy2

Small fluctuation of the HQ path


t

y

AdS/CFT computation

Static Quark:

straight string stretching to the horizon

v=0

u=e

We solve the small fluctuation problem

(mechanical problem)

u0=1

Horizon

In terms of the classical solution


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 => rescale the degrees of freedom

(Liu, Rajagopal, Wiedemann)


c(u)=v

u=1/g

Probe at finite velocity

t

Trailing string

=> work over tension

x=vt

x

same

k!

Drag valid for all p !

(Herzog, Karch, Kovtun, Kozcaz and Yaffe ; Gubser)

Broadening => repeat fluctuation problem

Depends on the energy of the probe!


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 N=4 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 .


Back up Slides


Computation of (Radiative Energy Loss)

t

L

r0

(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


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 (L>Lc) with Q2max=6ET.

At strong coupling


Noise from Microscopic Theory

HQ momentum relaxation time:

Consider times such that

microscopic force (random)

charge density

electric field


Heavy Quark Partition Function

McLerran, Svetitsky (82)

YM states

YM + Heavy Quark states

Integrating out the heavy quark

Polyakov Loop


Heavy Quark Partition Function

McLerran, Svetitsky (82)

YM states

YM + Heavy Quark states

Integrating out the heavy quark

Polyakov Loop


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 :


E(t1,y1)Dt1dy1

Since in k there is no time order:

E(t2,y2)Dt2dy2

Force Correlators from Wilson Lines

Integrating the Heavy Quark propagator:

Which is obtained from small fluctuations of the Wilson line


rab (-b/2, b/2; -T)A

Final distribution

Momentum Distribution

-T/2

+T/2

v

f0 (b)

ff (b)


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