Near Zone Navier-Stokes Analysis of Heavy Quark Jet Quenching in an $\mathcal{N}$ =4 SYM Plasma

TL;DR

This paper analyzes the near zone energy-momentum tensor of a supersonic heavy quark jet in a strongly-coupled plasma using Navier-Stokes hydrodynamics, revealing limitations at high velocities and implications for thermalization and flow patterns.

Contribution

It provides a detailed near zone analysis of jet quenching in $ ext{AdS/CFT}$, highlighting the breakdown of hydrodynamics at high velocities and the presence of coherent fields.

Findings

Hydrodynamics worsens with increasing quark velocity.

Non-hydrodynamical region is narrow at high velocities.

Flow near the quark differs from large-distance Mach cone patterns.

Abstract

The near zone energy-momentum tensor of a supersonic heavy quark jet moving through a strongly-coupled $\mathcal{N}=4$ SYM plasma is analyzed in terms of first-order Navier-Stokes hydrodynamics. It is shown that the hydrodynamical description of the near quark region worsens with increasing quark velocities. For realistic quark velocities, $v=0.99$, the non-hydrodynamical region is located at a narrow band surrounding the quark with a width of approximately $3/\pi T$ in the direction parallel to the quark's motion and with a length of roughly $10/\pi T$ in the perpendicular direction. Our results can be interpreted as an indication of the presence of coherent Yang-Mills fields where deviation from hydrodynamics is at its maximum. In the region where hydrodynamics does provide a good description of the system's dynamics, the flow velocity is so small that all the nonlinear terms can be dropped. Our results, which are compatible with the thermalization timescales extracted from elliptic flow measurements, suggest that if AdS/CFT provides a good description of the RHIC system, the bulk of the quenched jet energy has more than enough time to locally thermalize and become encoded in the collective flow. The resulting flow pattern close to the quark, however, is shown to be considerably different than the superposition of Mach cones and diffusion wakes observed at large distances.