The Energy Dependence of the Saturation Momentum from RG Improved BFKL Evolution

TL;DR

The paper addresses how the saturation momentum Q_s evolves with energy in QCD by employing a renormalization-group–improved BFKL framework with a saturation boundary modeled by a constant-amplitude condition. It leverages the ω-expansion to resum collinear enhancements, analyzes evolution along a perturbative critical line, and extracts the Y-dependence of Q_s through a derived boundary condition, finding a slowly varying λ_s ≈ 0.29–0.30 in the phenomenologically relevant region. Key insights include the significance of running coupling and nonlinear boundary effects, the near-GBW–like exponential growth of Q_s with Y, and a geometrical-scaling form for the dipole amplitude on the perturbative side. The absolute normalization of Q_s remains undetermined due to an overall multiplicative constant, but the results provide a consistent, RG-consistent description of saturation dynamics and scaling behavior relevant for high-energy scattering phenomenology.

Abstract

We study the energy dependence of the saturation momentum in the context of the collinearly improved Leading and Next to Leading BFKL evolution, and in the presence of saturation boundaries. We find that the logarithmic derivative of the saturation momentum is varying very slowly with Bjorken-x, and its value is in agreement with the Golec-Biernat and Wusthoff model in the relevant x region. The scaling form of the amplitude for dipole-dipole or dipole-hadron scattering in the perturbative side of the boundary is given.