Drag force to all orders in gradients

TL;DR

This paper derives a comprehensive all-order gradient expansion for the drag force on a heavy quark in a strongly coupled plasma, incorporating effects of medium flow gradients and extending into non-hydrodynamic regimes.

Contribution

It provides the first all-order gradient expansion of the drag force in strongly coupled plasmas, including explicit third-order results and a semi-analytic all-order approximation.

Findings

Drag force includes contributions from all orders of velocity gradients.

Explicit third-order gradient results are derived.

An approximate all-order semi-analytic expression is obtained.

Abstract

We study the energy loss of a heavy quark slowly moving through an evolving strongly coupled plasma. We use the linearized fluid/gravity correspondence to describe small perturbations of the medium flow with general spacetime dependence. This all order linearized hydrodynamics results in a drag force exerted on a heavy quark even when it is at rest with the fluid element. We show how the general contribution to the drag force can be derived order by order in the medium velocity gradients and provide explicit results valid up to the third order. We then obtain an approximate semi-analytic result for the drag force to all orders in the gradient expansion but linearized in the medium velocity. Thus, the effects of a class of hydrodynamic gradients on the drag force are re-summed, giving further insight into the dissipative properties of strongly coupled plasmas. The all order result allows us to study the drag force in the non-hydrodynamic regime of linear medium perturbations that vary rapidly in space and time.