The $m$'bottom-up parton system with two momentum scales

TL;DR

This paper extends the bottom-up thermalization model of gluon systems in heavy ion collisions by introducing a two-scale approach, providing a modified evolution scenario with different thermalization times and temperatures.

Contribution

It introduces a generalized $m$'bottom-up parton system with two momentum scales, modifying the original bottom-up thermalization scenario to account for a more complex evolution.

Findings

Modified thermalization time and temperature predictions.

Introduction of two additional momentum scales.

Interpolation between early anisotropic and final equilibrated states.

Abstract

One possible evolutionary scenario of the dense gluon system produced in an ultrarelativistic heavy ion collision is the bottom-up thermalization scenario, which describes the dynamics of the system shortly after the collision via the decay of originally produced hard gluons to soft ones through QCD branching processes. The soft gluons form a thermal bath that subsequently reaches thermalization and/or equilibration. There is a scaling solution to the bottom-up problem that interpolates between its early stage, which has a highly anisotropic gluon distribution, and its final stage of equilibration which occurs later. Such a solution depends on a single parameter, the so called momentum asymmetry parameter $\delta$. With this scaling solution, the bottom-up scenario gets modified and the evolving parton system, referred to as the $m$'bottom-up parton system throughout this paper, is described by this modification. The time evolution of the system in the original bottom-up ansatz is driven by the saturation scale, $Q_{s}$. However, for the $m$'bottom-up we generalize the ansatz of the evolution by introducing two additional momentum scales, which give a thermalization time and temperature of the soft gluon bath somewhat different from those obtained when the $m$'bottom-up matches onto the final stage of the original bottom-up scenario.