The Energy Dependence of the Saturation Momentum

TL;DR

Mueller and Triantafyllopoulos analyze the energy dependence of the saturation momentum Q_s in high-energy QCD using BFKL evolution with saturation boundaries. They introduce a diffusion with absorptive barrier framework to model unitarity constraints and derive Q_s(Y) for both fixed and running coupling, including new Y-dependent prefactors and scaling properties. In the fixed-coupling case, Q_s grows exponentially with Y and geometric scaling holds over a wide momentum range; in the running-coupling case, Y^{1/6} corrections appear and the scaling region is more restricted, with Q_s growing as exp(const√Y). The results imply target-independence of Q_s in the asymptotic regime and provide a coherent picture linking forward and non-forward scattering under saturation.

Abstract

We study BFKL evolution and, in particular, the energy dependence of the saturation momentum in the presence of saturation boundaries limiting the region of linear BFKL evolution. In the case of fixed coupling evolution we confirm the previously found exponential term in $Q_s(Y)$ and determine the prefactor $Y$ and $α$ dependences. In the running coupling case we find $Y^{1/6}$ corrections to the $Y^{1/2}$exponential behavior previously known. Geometrical scaling of the scattering amplitude is valid in a wide-range of momenta for fixed coupling evolution and in a more restricted region for running coupling evolution.