The unintegrated gluon distribution from the GBW and BGK models

The gluon distribution is obtained from the Golec-Biernat-Wu center dot\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\ddot{\textrm{u}}$$\end{document}sthoff (GBW) and Bartels, Golec-Biernat, and Kowalski (BGK) models at low x. We derive analytical results for the unintegrated color dipole gluon distribution function at small transverse momentum, which provides useful information to constrain the kt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{t}$$\end{document}-shape of the unintegrated gluon distribution in comparison with the unintegrated gluon distribution (UGD) models. The longitudinal proton structure function FL(x,Q2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{L}(x,Q<^>2)$$\end{document} from the kt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$k_{t}$$\end{document} factorization scheme, using the unintegrated gluon density, is computed. We compare the predictions for the on-shell and twist-2 corrections with the HERA data and the CJ15 parameterization method for FL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{L}$$\end{document}. We show that this method describes very well the experimental data within the on-shell and twist-2 framework. Effects of parameters on FL\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$F_{L}$$\end{document}, where charm contribution is taken into account, are investigated. These results are in good agreement with the data at fixed W.