On Drag Forces and Jet Quenching in Strongly Coupled Plasmas

TL;DR

The paper addresses how energy loss of a heavy quark in strongly coupled plasmas can be captured via holography by generalizing the trailing-string drag force to backgrounds with arbitrary metric and dilaton. It provides a compact expression for the drag force $\frac{dp}{dt} = -{v\over 2\pi \ell_s^2} e^{\phi/2} G_{xx}|_{z_v}$ with $ (G_{tt}+G_{xx}v^2)|_{z_v}=0$, and applies this to the cascading KS plasma to reveal a nontrivial $v$-dependence, while comparing to a jet-quenching parameter. In parallel, it computes $\hat{q}$ for a charged ${\cal N}=4$ plasma and contrasts it with the corresponding drag force, finding qualitative agreement at small charges but distinct full functional forms. The results illustrate that $\hat{q}$ and drag are closely related probes of energy dissipation in holographic plasmas, with temperature and chemical potential influencing mainly through the effective rank and charge.

Abstract

We compute the drag force experienced by a heavy quark that moves through plasma in a gauge theory whose dual description involves arbitrary metric and dilaton fields. As a concrete application, we consider the cascading gauge theory at temperatures high above the deconfining scale, where we obtain a drag force with a non-trivial velocity dependence. We compare our results with the jet-quenching parameter for the same theory, and find qualitative agreement between the two approaches. Conversely, we calculate the jet-quenching parameter for N=4 super-Yang-Mills with an R-charge density (or equivalently, a chemical potential), and compare our result with the corresponding drag force.

Figures (1)

• Figure 1: The function defined in (\ref{['CKTeq']}), which codifies the dependence of the drag force (\ref{['dragKT']}) on the velocity beyond the expected relativistic dependence $v/\sqrt{1-v^2}$ found already in ${\cal N}=4$ SYM.