An improved analysis of proton structure function F2(x,t) at small x

We report an improved analysis of Taylor approximated coupled DGLAP equations for singlet F2S(x,t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{2}^{S}(x,t)$\end{document} and gluon G(x,t) distributions at small x pursued in recent years. To that end, we assume a plausible t-dependent relation between the singlet and gluon distribution valid at small x and omit the boundary condition F2S(1,t)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$F_{2}^{S} (1, t) = 0$\end{document}, for any t which needs large x extrapolation of small x solution. We observe that in general two inequivalent t-evolutions of F2S(x,t)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ F_{2}^{S} (x, t)$\end{document} and G(x, t) are possible. Theoretical advantages of one over the other are discussed and compared with the recently compiled data in order to choose the best one. Phenomenological range of validity of solutions is also reported.