# Onset of hydrodynamics for a quark-gluon plasma from the evolution of moments of distribution functions

## TL;DR

This paper investigates the early evolution of a quark-gluon plasma in heavy-ion collisions, focusing on the transition to hydrodynamics through moments of the distribution function that measure momentum anisotropies.

## Contribution

It introduces a new set of moments that better quantify momentum anisotropies and their relation to viscous hydrodynamics during the pre-equilibrium phase.

## Key findings

- Moments are directly related to viscous corrections in hydrodynamics.
- Analytical solutions in relaxation time approximation are obtained.
- Numerical evolution within the small angle approximation is demonstrated.

## Abstract

The pre-equilibrium evolution of a quark-gluon plasma produced in a heavy-ion collision is studied in the framework of kinetic theory. We discuss the approach to local thermal equilibrium, and the onset of hydrodynamics, in terms of a particular set of moments of the distribution function. These moments quantify the momentum anisotropies to a finer degree than the commonly used ratio of longitudinal to transverse pressures. They are found to be in direct correspondence with viscous corrections of hydrodynamics, and provide therefore an alternative measure of these corrections in terms of the distortion of the momentum distribution. As an application, we study the evolution of these moments by solving the Boltzmann equation for a boost invariant expanding system, first analytically in the relaxation time approximation, and then numerically for a quark-gluon plasma within the small angle approximation to the collision kernel.