Toward Equilibration in the Early Stages After a High Energy Heavy Ion Collision

TL;DR

The paper analyzes how gluons produced in a high-energy heavy ion collision rapidly approach equilibration within a dense, saturated gluon regime. Using the McLerran-Venugopalan framework, it derives a rate equation for the transfer of momentum from transverse to longitudinal directions due to small-angle gluon-gluon scatterings among freed gluons, valid up to the onset of equilibration. It finds that equilibration begins during a predominantly one-dimensional expansion, with the onset time and momentum scale set by the saturation momentum $Q_s$, and it provides criteria and scaling for when the kinetic approach remains valid before genuine equilibration dynamics take over. Overall, the work offers analytic insight into early-time thermalization in dense gluon systems and complements numerical studies of heavy ion collisions.

Abstract

The early stages in the evolution of the gluons produced in the central region of a head-on high-energy heavy ion collision is studied. An equation is given for the rate of change of transverse momentum into longitudinal momentum where the longitudinal direction is along the collision axis. We are able to follow the system up to the time where equilibration seems to be setting in, but we are unable to actually follow the system as it reaches equilibrium.