# Presentation: 102171

## 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)t1y1

- E(t2,y2)t2y2

- Small fluctuation of the HQ path

## AdS/CFT computation

- u0=1

- v=0

- Horizon

- u=

- Static Quark:
- straight  string stretching to the horizon

- We solve the small fluctuation problem
- (mechanical problem)

- In terms of the classical solution

## Broadening and Diffusion in AdS/CFT

- In perturbation theory

- Depends explicitly on Nc.  Different from /s

- It is not universal!

- Putting numbers

- To compare with QCD => rescale the degrees of freedom

- (Liu, Rajagopal, Wiedemann)

## Probe at finite velocity

- x

- t

- x=vt

- Trailing string
-   => work over  tension

- same
-  

- 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 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 calculated  scales as        and takes much larger values than the perturbative extrapolation for QCD.

- The momentum broadening  at finite v diverges as        .

## Back up Slides

## Computation of       (Radiative Energy Loss)

- (Liu, Rajagopal, Wiedemann)

- Dipole amplitude:
-     two parallel Wilson lines in the light cone:

- For small transverse distance:

- Order of limits:

- String action becomes imaginary for

- entropy scaling

## Energy Dependence of  

- (JC & X. N. Wang)

- From the unintegrated PDF

- Evolution leads to growth of the gluon density,

- In the DLA

- Saturation effects 

- For an infinite conformal plasma (L>Lc) with Q2max=6ET.

- At strong coupling

- HTL provide the initial conditions for evolution.

## 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)

- Polyakov Loop

- YM + Heavy Quark states

- YM  states

- Integrating  out the heavy quark

## Heavy Quark Partition Function

- McLerran, Svetitsky  (82)

- Polyakov Loop

- YM + Heavy Quark states

- YM  states

- Integrating  out the heavy quark

##  as a Retarded Correlator

-  is defined as an unordered correlator:

- From ZHQ the only unordered correlator is

- Defining:

- In the 0 limit the contour dependence disappears :

## Force Correlators from Wilson Lines

- Which is obtained from small fluctuations of the Wilson line

- Integrating the Heavy Quark propagator:

## Momentum Distribution

- -T/2

- +T/2

- v

- f0 (b)

- ff (b)