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:0812.1051

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

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 192301 (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

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

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:

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

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

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

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

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)

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