1. Heavy-quark energy loss and thermalization in a strongly-coupled plasma
Cyrille Marquet
Columbia University
F. Dominguez, C. M., A. Mueller, B. Wu and B.-W. Xiao, Nucl. Phys. A811 (2008) 197
G. Beuf, C.M. and B.-W. Xiao, arXiv:

2. Introduction
what happens to a quark produced in the early stages of a heavy-ion collision ?
medium-induced
radiation
it loses energy in the plasma and may thermalize
it is unclear if the pQCD approach can describe the suppression of high-pT particles in Au+Au collisions:
in the case of light quarks, comparisons between models and data indicate the need for a large jet quenching parameter
however, for a weakly-coupled QCD plasma we expect

3. Motivations
in the case of heavy quarks, the dead-cone effect in pQCD implies a weaker suppression for heavier quarks
high-pT electrons from c and b decays indicate a similar suppression for light and heavy quarks
STAR, PRL (2007)
trend: models underestimate the suppression
the measurements do not distinguish the charm and bottom quark contributions in the future, separating these contributions would be helpful
for the N=4 SYM theory, the AdS/CFT correspondence allows to investigate the strong coupling regime
 this motivated to think about a strongly-coupled plasma
however the tools to address the QCD dynamics at strong coupling are limited

4. The AdS/CFT correspondence
the N=4 SYM theory: 1 gauge field, 4 fermions, 6 scalars, all adjoint
in the large Nc limit, the ‘t Hooft coupling λ controls the theory
strong coupling means ‘t Hooft limit in gauge theory:
the equivalent string theory in AdS5 x S5 : weak coupling and small curvature
classical gravity is a good approximation
fifth dimension
curvature radius of AdS5
T = Hawking temperature of the black
hole = temperature of the SYM plasma
the SYM theory lives on the boundary at r = infinity
horizon
the AdS5 black-hole metric
the quantum dynamics of the SYM theory is mapped into a fifth dimension

5. A heavy quark in the SYM plasma
the flavor brane
a heavy quark lives on a brane at
with a string attached to it, hanging down to the horizon
the string dynamics is given by the Nambu-Goto action:
area of the string worldsheet
induced metric on the worldsheet
equation of motion:
rate at which energy flows down the string:
parameterization:

6. The trailing string picture
the string shape and energy flow
the string shape when the quark is being pulled at a
constant velocity v:
corresponding rate of energy flow down the string:
black-hole horizon with Hawking
temperature T = temperature of the SYM plasma
Herzog et al (2006), Gubser et al (2006), Liu et al (2006)
points on the string can be identified to fluctuations in the heavy quark wave function with virtuality ~ u
the string is dual to a dressed quark
the part of string above is genuinely part of heavy quark
the part of string below is emitted radiation
on the gauge theory side
is the saturation scale

7. The energy of the dressed quark
the energy of the upper part of the string
from
our definition of the
thermal quark mass
energy conservation
energy changes due to the variation of us
energy flow at us ≡ energy
radiated into the plasma
energy flow at um ≡ work of
external forces on the quark
from

8. Letting the quark go the trailing string case
stationary problem
the energy flow is constant along the string, so it doesn’t matter where the energy loss is evaluated
letting the quark slow down
no external forces
now there is a time dependence
perturbative calculation in the large mass limit
what is the radiative energy loss ?
now the energy flow varies along the string, it was important to determine where the energy loss should be evaluated

9. Deformation of the trailing string
first order results
the correction to the shape of the trailing string
the thermal mass of the heavy quark
the radiative energy loss
second order results

10. Heavy-quark thermalization
the deceleration of the quark is controlled by the energy loss
this gives the following equation
we estimate the thermalization time:
this is compared with the guess
Herzog et al (2006)

11. Conclusions
same parametric form for the heavy-quark energy loss when written in terms of the saturation scale Qs
the saturation scales differ between weakly-coupled QCD and strongly-coupled SYM theories
the plasma length L dependence is stronger in SYM compared to pQCD, which goes in the right direction to explain RHIC data
at strong coupling the time scale for heavy quark thermalization is