The unintegrated gluon distribution from the modified BK equation

We investigate the recently proposed non-linear equation for the unintegrated gluon distribution function which includes the subleading effects at small x. We obtained numerically the solution to this equation in (x,k) space, and also the integrated gluon density. The subleading effects affect strongly the normalization and the x and k dependence of the gluon distribution. We show that the saturation scale Qs(x), which is obtained from this model, is consistent with the one used in the saturation model by Golec-Biernat and Wüsthoff. We also estimate the non-linear effects by looking at the relative normalization of the solutions to the linear and non-linear equations. It turns out that the differences are quite large even in the nominally dilute regime, that is when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$Q^2 \gg Q_{\mathrm {s}}^2$\end{document}. Finally, we calculate the dipole-nucleon cross section.