Saturation and linear transport equation

TL;DR

This paper demonstrates that the GBW saturation model exactly solves the one-dimensional linear transport equation and connects it to the BK equation in the saturated regime, highlighting the balance of diffusion, splitting, and nonlinear effects.

Contribution

It establishes a direct link between the GBW saturation model and the linear transport equation, providing a new perspective on nonlinear QCD evolution equations.

Findings

GBW model is an exact solution to the linear transport equation

Connection between the BK equation and the transport equation in saturation regime

Balance of diffusion, splitting, and nonlinear terms in the model

Abstract

We show that the GBW saturation model provides an exact solution to the one dimensional linear transport equation. We also show that it is motivated by the BK equation considered in the saturated regime when the diffusion and the splitting term in the diffusive approximation are balanced by the nonlinear term.