Chromohydrodynamical instabilities induced by relativistic jets

TL;DR

This paper investigates how relativistic jets induce chromohydrodynamical instabilities in quark-gluon plasma, revealing conditions for instability and proposing a mechanism for jet quenching through excitation of unstable modes.

Contribution

It derives dispersion laws for unstable collective modes in a hydrodynamical framework, analyzing their dependence on jet velocity, momentum, and angle, which is a novel approach.

Findings

Unstable modes occur for jet velocities exceeding the plasma's sound speed.

Modes with small momenta are unstable, while ultrarelativistic jets stabilize longitudinal modes.

Most unstable modes occur at angles greater than π/8 between jet velocity and mode momentum.

Abstract

We study the properties of the chromohydrodynamical instabilities induced by a relativistic jet that crosses the quark-gluon plasma. Assuming that the jet of particles and the plasma can be described using a hydrodynamical approach, we derive and discuss the dispersion laws for the unstable collective modes. In our analysis the chromohydrodynamical equations for the collective modes are tackled in the linear response approximation. Such an approximation, valid for short time scales, allows to study in a straightforward way the dependence of the dispersion laws of the collective modes on the velocity of the jet, on the magnitude of the momentum of the collective mode and on the angle between these two quantities. We find that unstable modes arise for velocity of the jet larger than the speed of the sound of the plasma and only modes with momenta smaller than a certain values are unstable. Moreover, for ultrarelativistic velocities of the jet the longitudinal mode becomes stable and the most unstable modes correspond to relative angles between the velocity of the jet and momentum of the collective mode larger than $\sim \pi/8$. Our results suggest an alternative mechanism for the description of the jet quenching phenomenon, where the jet crossing the plasma loses energy exciting colored unstable modes.