Gluon Transport Equation in the Small Angle Approximation and the Onset of Bose-Einstein Condensation

TL;DR

This paper models the evolution of dense gluon systems in heavy ion collisions using a small angle approximation of the Boltzmann equation with Bose statistics, demonstrating conditions for Bose-Einstein condensation.

Contribution

It introduces a transport equation approach to study gluon thermalization and Bose-Einstein condensation in a simplified, uniform system ignoring inelastic processes.

Findings

Overpopulated systems reach Bose-Einstein condensation in finite time.

System evolves towards thermal equilibrium for low initial densities.

Scaling behavior characterizes the approach to condensation.

Abstract

In this paper, we study the evolution of a dense system of gluons, such as those produced in the early stages of ultra-relativistic heavy ion collisions. We describe the approach to thermal equilibrium using the small angle approximation for gluon scattering in a Boltzmann equation that includes the effects of Bose statistics. In the present study we ignore the effect of the longitudinal expansion, i.e., we restrict ourselves to spatially uniform systems, with spherically symmetric momentum distributions. Furthermore we take into account only elastic scattering, i.e., we neglect inelastic, number changing, processes. We solve the transport equation for various initial conditions that correspond to small or large initial gluon phase-space densities. For a small initial phase-space density, the system evolves towards thermal equilibrium, as expected. For a large enough initial phase-space density the equilibrium state contains a Bose condensate. We present numerical evidence that such over-populated systems reach the onset of Bose-Einstein condensation in a finite time. The approach to condensation is characterized by a scaling behavior that we briefly analyze.