Pomeron fan diagrams with an infrared cutoff and running coupling
M. A. Braun
TL;DR
The paper investigates non-linear pomeron fan evolution for a large nucleus at small $x$, focusing on infrared behavior and the running of $\alpha_s$. It solves the non-linear equation $(\partial/\partial y + H)\phi(y,k) = -\phi^2(y,k)$ with an infrared cutoff and a running coupling, comparing fixed and running scenarios. The infrared cutoff has only minor quantitative effects on the saturation momentum $Q_s(y)$ and gluon density, while running coupling markedly slows $Q_s(y)$ growth from exponential to a slower form and reduces the structure function by up to an order of magnitude, with approximate $z$-scaling $z=k/Q_s(y)$ preserved. These results improve the physical realism of the evolution, resolve unphysically large $Q_s$ from fixed-coupling, uncut dynamics, and reinforce the infrared stability of the non-linear approach for high-energy nuclear QCD.
Abstract
By direct numerical calculations the influence of a physically relevant infrared cutoff and running coupling on the gluon density and structure function of a large nucleus is studied in the perturbative QCD approach. It is found that the infrared cutoff changes the solutions very little. Running of the coupling produces a bigger change, considerably lowering both the saturation momentum and values of the structure functions.